Pub Date : 1900-01-01DOI: 10.1070/IM1994v043n01ABEH001554
Vyacheslav A Krasnov
For an algebraic cycle on a real algebraic GM-manifold , the relationship between the homology classes and is studied. It is shown that similar relations hold for smooth cycles on a GM-surface. The results are applied to prove congruences for the Euler characteristic of the set .
{"title":"ALGEBRAIC CYCLES ON A REAL ALGEBRAIC GM-MANIFOLD AND THEIR APPLICATIONS","authors":"Vyacheslav A Krasnov","doi":"10.1070/IM1994v043n01ABEH001554","DOIUrl":"https://doi.org/10.1070/IM1994v043n01ABEH001554","url":null,"abstract":"For an algebraic cycle on a real algebraic GM-manifold , the relationship between the homology classes and is studied. It is shown that similar relations hold for smooth cycles on a GM-surface. The results are applied to prove congruences for the Euler characteristic of the set .","PeriodicalId":158473,"journal":{"name":"Russian Academy of Sciences. Izvestiya Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128993178","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 : 1900-01-01DOI: 10.1070/IM1995v044n02ABEH001596
V I Bakhtin
For a sequence of smooth mappings of a Riemannian manifold, which is a nonstationary analogue of a hyperbolic dynamical system, a compatible sequence of measures carrying one into another under the mappings is constructed. A geometric interpretation is given for these measures, and it is proved that they depend smoothly on the parameter. The central limit theorem is proved for a sequence of smooth functions on the manifold with respect to these measures; it is shown that the correlations decrease exponentially, and an exponential estimate like Bernstein's inequality is obtained for probabilities of large deviations.
{"title":"RANDOM PROCESSES GENERATED BY A HYPERBOLIC SEQUENCE OF MAPPINGS. I","authors":"V I Bakhtin","doi":"10.1070/IM1995v044n02ABEH001596","DOIUrl":"https://doi.org/10.1070/IM1995v044n02ABEH001596","url":null,"abstract":"For a sequence of smooth mappings of a Riemannian manifold, which is a nonstationary analogue of a hyperbolic dynamical system, a compatible sequence of measures carrying one into another under the mappings is constructed. A geometric interpretation is given for these measures, and it is proved that they depend smoothly on the parameter. The central limit theorem is proved for a sequence of smooth functions on the manifold with respect to these measures; it is shown that the correlations decrease exponentially, and an exponential estimate like Bernstein's inequality is obtained for probabilities of large deviations.","PeriodicalId":158473,"journal":{"name":"Russian Academy of Sciences. Izvestiya Mathematics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127309343","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 : 1900-01-01DOI: 10.1070/IM1993v041n01ABEH002182
Dmitri Orlov
This paper studies derived categories of coherent sheaves on varieties that are obtained by projectivization of vector bundles and by monoidal transformations. Conditions for the existence of complete exceptional sets in such categories are derived; they give new examples of varieties on which exceptional sets exist.
{"title":"PROJECTIVE BUNDLES, MONOIDAL TRANSFORMATIONS, AND DERIVED CATEGORIES OF COHERENT SHEAVES","authors":"Dmitri Orlov","doi":"10.1070/IM1993v041n01ABEH002182","DOIUrl":"https://doi.org/10.1070/IM1993v041n01ABEH002182","url":null,"abstract":"This paper studies derived categories of coherent sheaves on varieties that are obtained by projectivization of vector bundles and by monoidal transformations. Conditions for the existence of complete exceptional sets in such categories are derived; they give new examples of varieties on which exceptional sets exist.","PeriodicalId":158473,"journal":{"name":"Russian Academy of Sciences. Izvestiya Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114359757","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 : 1900-01-01DOI: 10.1070/IM1993v040n02ABEH002167
V Ya Pidstrigach, A N Tyurin
We construct invariants of the smooth structure of an algebraic surface in terms of coupled Dirac operators. The invariants allow us to distinguish between del Pezzo surfaces and fake del Pezzo surfaces by their smooth structure.
{"title":"INVARIANTS OF THE SMOOTH STRUCTURE OF AN ALGEBRAIC SURFACE ARISING FROM THE DIRAC OPERATOR","authors":"V Ya Pidstrigach, A N Tyurin","doi":"10.1070/IM1993v040n02ABEH002167","DOIUrl":"https://doi.org/10.1070/IM1993v040n02ABEH002167","url":null,"abstract":"We construct invariants of the smooth structure of an algebraic surface in terms of coupled Dirac operators. The invariants allow us to distinguish between del Pezzo surfaces and fake del Pezzo surfaces by their smooth structure.","PeriodicalId":158473,"journal":{"name":"Russian Academy of Sciences. Izvestiya Mathematics","volume":"376 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129095683","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 : 1900-01-01DOI: 10.1070/IM1993v040n01ABEH001851
D V Alekseevskiĭ, M M Graev
The authors distinguish a class of twistor spaces that are associated, following Bérard-Bergery and Ochiai, with -structures on even-dimensional manifolds and connections in . It is assumed that is a complex totally geodesic submanifold of the affine symmetric space . This class includes all the basic examples of twistor spaces fibered over an even-dimensional base. The integrability of the canonical almost complex structure and the holomorphy of the canonical distribution in are studied in terms of some natural -structure with a connection on the manifold . Some examples are also treated.
{"title":"TWISTORS AND -STRUCTURES","authors":"D V Alekseevskiĭ, M M Graev","doi":"10.1070/IM1993v040n01ABEH001851","DOIUrl":"https://doi.org/10.1070/IM1993v040n01ABEH001851","url":null,"abstract":"The authors distinguish a class of twistor spaces that are associated, following Bérard-Bergery and Ochiai, with -structures on even-dimensional manifolds and connections in . It is assumed that is a complex totally geodesic submanifold of the affine symmetric space . This class includes all the basic examples of twistor spaces fibered over an even-dimensional base. The integrability of the canonical almost complex structure and the holomorphy of the canonical distribution in are studied in terms of some natural -structure with a connection on the manifold . Some examples are also treated.","PeriodicalId":158473,"journal":{"name":"Russian Academy of Sciences. Izvestiya Mathematics","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123875705","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 : 1900-01-01DOI: 10.1070/IM1994v043n02ABEH001565
M Z Shapiro
A curve on a sphere or on a projective space is called nondegenerate if it has a nondegenerate moving frame at every point. The number of homotopy classes of closed nondegenerate curves immersed in the sphere or projective space is computed. In the case of the sphere Sn, this turns out to be 4 for odd n≥3 and 6 for even n≥2; in the case of the projective space Pn, 10 for odd n≥3 and 3 for even n≥2.
{"title":"TOPOLOGY OF THE SPACE OF NONDEGENERATE CURVES","authors":"M Z Shapiro","doi":"10.1070/IM1994v043n02ABEH001565","DOIUrl":"https://doi.org/10.1070/IM1994v043n02ABEH001565","url":null,"abstract":"A curve on a sphere or on a projective space is called nondegenerate if it has a nondegenerate moving frame at every point. The number of homotopy classes of closed nondegenerate curves immersed in the sphere or projective space is computed. In the case of the sphere Sn, this turns out to be 4 for odd n≥3 and 6 for even n≥2; in the case of the projective space Pn, 10 for odd n≥3 and 3 for even n≥2.","PeriodicalId":158473,"journal":{"name":"Russian Academy of Sciences. Izvestiya Mathematics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115837093","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 : 1900-01-01DOI: 10.1070/IM1995v044n01ABEH001589
V V Andrievskiĭ, V V Maĭmeskul
Three classes of functions are introduced, corresponding to known results in the theory of uniform polynomial approximation of functions on arcs in the complex plane. The structural properties of functions in these classes are described from a unified point of view, which allows one to understand more fully their nature and the differences between them.
{"title":"CONSTRUCTIVE DESCRIPTION OF CERTAIN CLASSES OF FUNCTIONS ON QUASISMOOTH ARCS","authors":"V V Andrievskiĭ, V V Maĭmeskul","doi":"10.1070/IM1995v044n01ABEH001589","DOIUrl":"https://doi.org/10.1070/IM1995v044n01ABEH001589","url":null,"abstract":"Three classes of functions are introduced, corresponding to known results in the theory of uniform polynomial approximation of functions on arcs in the complex plane. The structural properties of functions in these classes are described from a unified point of view, which allows one to understand more fully their nature and the differences between them.","PeriodicalId":158473,"journal":{"name":"Russian Academy of Sciences. Izvestiya Mathematics","volume":"144 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116562611","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 : 1900-01-01DOI: 10.1070/IM1995v045n02ABEH001645
V I Trofimov
This article is devoted to a positive solution, announced earlier by the author, of the question of boundedness of orders of stabilizers of vertices of connected finite symmetric graphs with projective suborbits. The case when the characteristic of the field is 3 and the automorphism group of the graph acts intransitively on its 3-arcs is considered. (The case when the characteristic of the field is 3 and the group acts transitively on the 3-arcs of the graph will be considered in Part II of this paper.) In parallel, some cases of a field of characteristic 2 are studied.
{"title":"GRAPHS WITH PROJECTIVE SUBORBITS. CASES OF SMALL CHARACTERISTICS. I","authors":"V I Trofimov","doi":"10.1070/IM1995v045n02ABEH001645","DOIUrl":"https://doi.org/10.1070/IM1995v045n02ABEH001645","url":null,"abstract":"This article is devoted to a positive solution, announced earlier by the author, of the question of boundedness of orders of stabilizers of vertices of connected finite symmetric graphs with projective suborbits. The case when the characteristic of the field is 3 and the automorphism group of the graph acts intransitively on its 3-arcs is considered. (The case when the characteristic of the field is 3 and the group acts transitively on the 3-arcs of the graph will be considered in Part II of this paper.) In parallel, some cases of a field of characteristic 2 are studied.","PeriodicalId":158473,"journal":{"name":"Russian Academy of Sciences. Izvestiya Mathematics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126461253","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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