Pub Date : 1991-06-30DOI: 10.1070/IM1991V036N03ABEH002038
A. Loboda
In this article we consider the problem of uniqueness of so-called normal coordinates for real-analytic generating manifolds of codimension 2 in C4. For nonumbilic surfaces we find a class of coordinates which is preserved only by linear transformations.
{"title":"LINEARIZABILITY OF HOLOMORPHIC MAPPINGS OF GENERATING MANIFOLDS OF CODIMENSION 2 IN C4","authors":"A. Loboda","doi":"10.1070/IM1991V036N03ABEH002038","DOIUrl":"https://doi.org/10.1070/IM1991V036N03ABEH002038","url":null,"abstract":"In this article we consider the problem of uniqueness of so-called normal coordinates for real-analytic generating manifolds of codimension 2 in C4. For nonumbilic surfaces we find a class of coordinates which is preserved only by linear transformations.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122333573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1991-06-30DOI: 10.1070/IM1991V036N03ABEH002030
I. V. Artamkin
This paper investigates the question of removability of singularities of torsion-free sheaves on algebraic surfaces in the universal deformation and the existence in it of a nonempty open set of locally free sheaves, and describes the tangent cone to the set of sheaves having degree of singularities larger than a given one. These results are used to prove that quasitrivial sheaves on an algebraic surface with (r + 1) max(1, p_g(X))$ SRC=http://ej.iop.org/images/0025-5726/36/3/A01/tex_im_2030_img3.gif/> have a universal deformation whose general sheaf is locally free and stable relative to any ample divisor on , and thereby to find a nonempty component of the moduli space of stable bundles on with and max(1, p_g(X) cdot (r + 1))$ SRC=http://ej.iop.org/images/0025-5726/36/3/A01/tex_im_2030_img5.gif/> on any algebraic surface. Bibliography: 11 titles.
{"title":"DEFORMING TORSION-FREE SHEAVES ON AN ALGEBRAIC SURFACE","authors":"I. V. Artamkin","doi":"10.1070/IM1991V036N03ABEH002030","DOIUrl":"https://doi.org/10.1070/IM1991V036N03ABEH002030","url":null,"abstract":"This paper investigates the question of removability of singularities of torsion-free sheaves on algebraic surfaces in the universal deformation and the existence in it of a nonempty open set of locally free sheaves, and describes the tangent cone to the set of sheaves having degree of singularities larger than a given one. These results are used to prove that quasitrivial sheaves on an algebraic surface with (r + 1) max(1, p_g(X))$ SRC=http://ej.iop.org/images/0025-5726/36/3/A01/tex_im_2030_img3.gif/> have a universal deformation whose general sheaf is locally free and stable relative to any ample divisor on , and thereby to find a nonempty component of the moduli space of stable bundles on with and max(1, p_g(X) cdot (r + 1))$ SRC=http://ej.iop.org/images/0025-5726/36/3/A01/tex_im_2030_img5.gif/> on any algebraic surface. Bibliography: 11 titles.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132978711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1991-04-30DOI: 10.1070/IM1991V037N02ABEH002073
Pezzo Surfaces, V. Alekseev
P ROOF . By Proposition 1.3 the cone of effective curves on X is generated by finitely many curves. From the formula K~ = n*Kx + Y^aiFi it follows that the divisor ~MK~ is effective for some positive integer Μ. Let C be an irreducible reduced curve with C < 0. We now carry out the following procedure: if / Φ C is an exceptional curve of genus 1 and C • I < 1, then we contract this curve. We repeat this procedure several times until we obtain a morphism / : X > 5" with the following properties: S is a nonsingular surface, C{ — / (C ) is a nonsingular curve and for any curve Ι Φ Cx of genus 1 we have Cx • I > 2. If S = P 2 or F n , η < Ν, then C 2 > Ν and C 2 > c k > N k. If C > 3 , then C > 3 k . Now suppose S φ Ρ 2 , F n and c < 4 . We prove that the divisor 2KS + Cx is numerically effective. The cone of effective curves on the surface S is generated by finitely many curves; let {E^ be a minimal system of generators. If Ks · £J. > 0 and Et φ C, , then {2KS + Cx ) Ei> 0. If Ks • Ei < 0 and Ei φ C, , then Ej is an exceptional curve of genus 1 and {2KS + C, )·£ ,• > 0. Finally, {2KS + C,) · C{ = 4/ 7 Q(C, ) 4 C >0 . Thus, the divisor 2KS + Cx is numerically effective and the divisor —MKS =
{"title":"CORRECTION TO THE PAPER “FRACTIONAL INDICES OF LOG DEL PEZZO SURFACES”","authors":"Pezzo Surfaces, V. Alekseev","doi":"10.1070/IM1991V037N02ABEH002073","DOIUrl":"https://doi.org/10.1070/IM1991V037N02ABEH002073","url":null,"abstract":"P ROOF . By Proposition 1.3 the cone of effective curves on X is generated by finitely many curves. From the formula K~ = n*Kx + Y^aiFi it follows that the divisor ~MK~ is effective for some positive integer Μ. Let C be an irreducible reduced curve with C < 0. We now carry out the following procedure: if / Φ C is an exceptional curve of genus 1 and C • I < 1, then we contract this curve. We repeat this procedure several times until we obtain a morphism / : X > 5\" with the following properties: S is a nonsingular surface, C{ — / (C ) is a nonsingular curve and for any curve Ι Φ Cx of genus 1 we have Cx • I > 2. If S = P 2 or F n , η < Ν, then C 2 > Ν and C 2 > c k > N k. If C > 3 , then C > 3 k . Now suppose S φ Ρ 2 , F n and c < 4 . We prove that the divisor 2KS + Cx is numerically effective. The cone of effective curves on the surface S is generated by finitely many curves; let {E^ be a minimal system of generators. If Ks · £J. > 0 and Et φ C, , then {2KS + Cx ) Ei> 0. If Ks • Ei < 0 and Ei φ C, , then Ej is an exceptional curve of genus 1 and {2KS + C, )·£ ,• > 0. Finally, {2KS + C,) · C{ = 4/ 7 Q(C, ) 4 C >0 . Thus, the divisor 2KS + Cx is numerically effective and the divisor —MKS =","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127418975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1991-04-30DOI: 10.1070/IM1991V037N02ABEH002071
E. Zelenyuk, I. Protasov
A filter on an abelian group G is called a T-filter if there exists a Hausdorff group topology under which converges to zero. G{} will denote the group G with the largest topology among those making converge to zero. This method of defining a group topology is completely equivalent to the definition of an abstract group by defining relations. We shall obtain characterizations of T-filters and of T-sequences; among these, we shall pay particular attention to T-sequences on the integers. The method of T-sequences will be used to construct a series of counterexamples for several open problems in topological algebra. For instance there exists, on every infinite abelian group, a topology distinguishing between sequentiality and the Frechet-Urysohn property (this solves a problem posed by V.I. Malykhin); we also find a topology on the group of integers admitting no nontrivial continuous character, thus solving a problem of Nienhuys. We show also that on every infinite abelian group there exists a free ultrafilter which is not a T-ultrafilter.
{"title":"Topologies on Abelian Groups","authors":"E. Zelenyuk, I. Protasov","doi":"10.1070/IM1991V037N02ABEH002071","DOIUrl":"https://doi.org/10.1070/IM1991V037N02ABEH002071","url":null,"abstract":"A filter on an abelian group G is called a T-filter if there exists a Hausdorff group topology under which converges to zero. G{} will denote the group G with the largest topology among those making converge to zero. This method of defining a group topology is completely equivalent to the definition of an abstract group by defining relations. We shall obtain characterizations of T-filters and of T-sequences; among these, we shall pay particular attention to T-sequences on the integers. The method of T-sequences will be used to construct a series of counterexamples for several open problems in topological algebra. For instance there exists, on every infinite abelian group, a topology distinguishing between sequentiality and the Frechet-Urysohn property (this solves a problem posed by V.I. Malykhin); we also find a topology on the group of integers admitting no nontrivial continuous character, thus solving a problem of Nienhuys. We show also that on every infinite abelian group there exists a free ultrafilter which is not a T-ultrafilter.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125519340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1991-04-30DOI: 10.1070/IM1991V036N02ABEH002024
L. Kuz'min
For an -extension of an algebraic number field satisfying certain appropriate conditions the author obtains a formula analogous to the Riemann-Hurwitz formula. This formula connects the Iwasawa invariants of the fields and , where is some -extension of the field . It is not assumed that and are fields of CM-type.
{"title":"AN ANALOG OF THE RIEMANN-HURWITZ FORMULA FOR ONE TYPE OF $ l$-EXTENSION OF ALGEBRAIC NUMBER FIELDS","authors":"L. Kuz'min","doi":"10.1070/IM1991V036N02ABEH002024","DOIUrl":"https://doi.org/10.1070/IM1991V036N02ABEH002024","url":null,"abstract":"For an -extension of an algebraic number field satisfying certain appropriate conditions the author obtains a formula analogous to the Riemann-Hurwitz formula. This formula connects the Iwasawa invariants of the fields and , where is some -extension of the field . It is not assumed that and are fields of CM-type.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"614 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116210157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1991-04-30DOI: 10.1070/IM1991V036N02ABEH002027
A. Samoilenko, R. I. Petrishin
Conditions are found for the existence of an integral manifold for a nonlinear oscillatory system with slowly varying frequencies, and an algorithm for constructing it is described. A theorem is proved on the conditional asymptotic stability of the integral manifold with respect to a set of initial values for the slow variables. Smoothness is also studied, and bounds on the partial derivatives of the function that describes the integral manifold are obtained.
{"title":"ON INTEGRAL MANIFOLDS OF MULTIFREQUENCY OSCILLATORY SYSTEMS","authors":"A. Samoilenko, R. I. Petrishin","doi":"10.1070/IM1991V036N02ABEH002027","DOIUrl":"https://doi.org/10.1070/IM1991V036N02ABEH002027","url":null,"abstract":"Conditions are found for the existence of an integral manifold for a nonlinear oscillatory system with slowly varying frequencies, and an algorithm for constructing it is described. A theorem is proved on the conditional asymptotic stability of the integral manifold with respect to a set of initial values for the slow variables. Smoothness is also studied, and bounds on the partial derivatives of the function that describes the integral manifold are obtained.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"198 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121617623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1991-04-30DOI: 10.1070/IM1991V037N02ABEH002064
V. K. Zakharov
A new algebraic structure of a -ring with refinement and a new topological structure of an -space with cover are introduced. On the basis of them the notions of divisible hulls and surrounded coverings of certain types are introduced. With the help of these notions the Lebesgue extension and the Borel extension of the first class are given a ring characterization as divisible hulls of a certain type (Theorem 1); preimages of maximal ideals of these extensions are given a topological characterization as surrounded coverings of a certain type (Theorem 2).
{"title":"CONNECTIONS BETWEEN THE LEBESGUE EXTENSION AND THE BOREL EXTENSION OF THE FIRST CLASS, AND BETWEEN THE PREIMAGES CORRESPONDING TO THEM","authors":"V. K. Zakharov","doi":"10.1070/IM1991V037N02ABEH002064","DOIUrl":"https://doi.org/10.1070/IM1991V037N02ABEH002064","url":null,"abstract":"A new algebraic structure of a -ring with refinement and a new topological structure of an -space with cover are introduced. On the basis of them the notions of divisible hulls and surrounded coverings of certain types are introduced. With the help of these notions the Lebesgue extension and the Borel extension of the first class are given a ring characterization as divisible hulls of a certain type (Theorem 1); preimages of maximal ideals of these extensions are given a topological characterization as surrounded coverings of a certain type (Theorem 2).","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123498894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1991-04-30DOI: 10.1070/IM1991V037N02ABEH002074
A. Vdovin
A new axiomatic set theory, consisting of four axioms, is presented. In this theory one can prove as theorems all of the axioms of Zermelo-Fraenkel set theory with the axiom of choice (ZFC), except for the axiom of regularity.
{"title":"FOUNDATIONS OF A NEW AXIOMATIC SET THEORY","authors":"A. Vdovin","doi":"10.1070/IM1991V037N02ABEH002074","DOIUrl":"https://doi.org/10.1070/IM1991V037N02ABEH002074","url":null,"abstract":"A new axiomatic set theory, consisting of four axioms, is presented. In this theory one can prove as theorems all of the axioms of Zermelo-Fraenkel set theory with the axiom of choice (ZFC), except for the axiom of regularity.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127485094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1991-04-30DOI: 10.1070/IM1991V036N02ABEH002029
É. M. Galeev
The order of Kolmogorov widths are determined for the class that is the intersection of classes of periodic functions of one variable of "higher" smoothness, in the space for , and estimates from above for "low" smoothness, and also the order of Kolmogorov widths is calculated for periodic functions of several variables in the space for . The estimate from below for reduces to the estimate from below of the width of a finite-dimensional set whose width is determined. Bibliography: 28 titles.
{"title":"KOLMOGOROV WIDTHS OF CLASSES OF PERIODIC FUNCTIONS OF ONE AND SEVERAL VARIABLES","authors":"É. M. Galeev","doi":"10.1070/IM1991V036N02ABEH002029","DOIUrl":"https://doi.org/10.1070/IM1991V036N02ABEH002029","url":null,"abstract":"The order of Kolmogorov widths are determined for the class that is the intersection of classes of periodic functions of one variable of \"higher\" smoothness, in the space for , and estimates from above for \"low\" smoothness, and also the order of Kolmogorov widths is calculated for periodic functions of several variables in the space for . The estimate from below for reduces to the estimate from below of the width of a finite-dimensional set whose width is determined. Bibliography: 28 titles.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"210 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116438003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1991-04-30DOI: 10.1070/IM1991V037N02ABEH002070
E. Shustin
Two geometrical constructions are given which enable one to rule out certain arrangements of ovals of real plane curves of degree a multiple of 8. In particular, for degree 8 one cannot have an M-curve for which one oval envelopes the other ovals.
{"title":"NEW RESTRICTIONS ON THE TOPOLOGY OF REAL CURVES OF DEGREE A MULTIPLE OF 8","authors":"E. Shustin","doi":"10.1070/IM1991V037N02ABEH002070","DOIUrl":"https://doi.org/10.1070/IM1991V037N02ABEH002070","url":null,"abstract":"Two geometrical constructions are given which enable one to rule out certain arrangements of ovals of real plane curves of degree a multiple of 8. In particular, for degree 8 one cannot have an M-curve for which one oval envelopes the other ovals.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"22 45","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132271884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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