We consider the influence of the number of separated maximum points and Valiron deficiency over the magnitude of Petrenko's deviation of algebroid functions of finite lower order. Presented results are the generalization of Petrenko's and Niino's results. We also give examples showing that the estimates are sharp.
{"title":"On deviations and maximum points of algebroid functions of finite lower order","authors":"A. Kowalski, I. Marchenko","doi":"10.2996/kmj44103","DOIUrl":"https://doi.org/10.2996/kmj44103","url":null,"abstract":"We consider the influence of the number of separated maximum points and Valiron deficiency over the magnitude of Petrenko's deviation of algebroid functions of finite lower order. Presented results are the generalization of Petrenko's and Niino's results. We also give examples showing that the estimates are sharp.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49420698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we discuss an asymptotic boundary behavior of the complete Kahler-Einstein metric of negative Ricci curvature on a quasi-projective manifold with semiample log-canonical bundle. In particular, we focus our attention on its relations with degeneration of positivity for the log-canonical bundle on the boundary divisor. Based on a pioneering result due to G. Schumacher, a fundamental conjecture about the relations is proposed in this paper. Moreover it is also proved that the conjecture actually holds in the case when the boundary divisor is of general type.
{"title":"Boundary behavior of Kähler-Einstein metric of negative ricci curvature over quasi-projective manifolds with boundary of general type","authors":"Shin Kikuta","doi":"10.2996/kmj44106","DOIUrl":"https://doi.org/10.2996/kmj44106","url":null,"abstract":"In this paper, we discuss an asymptotic boundary behavior of the complete Kahler-Einstein metric of negative Ricci curvature on a quasi-projective manifold with semiample log-canonical bundle. In particular, we focus our attention on its relations with degeneration of positivity for the log-canonical bundle on the boundary divisor. Based on a pioneering result due to G. Schumacher, a fundamental conjecture about the relations is proposed in this paper. Moreover it is also proved that the conjecture actually holds in the case when the boundary divisor is of general type.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44592261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Hurwitz metric was recently defined by Minda by considering a variational problem that involves holomorphic maps from the disc that are globally injective at the origin. In this note, sharp boundary estimates for this metric are obtained on $C^2$-smooth planar domains and as a consequence, it is shown that it is uniformly comparable with the Caratheodory and Kobayashi metrics on such domains. In addition, estimates for the generalized curvatures of this metric are also given.
{"title":"On the Hurwitz metric","authors":"Amar Deep Sarkar, Kaushal Verma","doi":"10.2996/KMJ44108","DOIUrl":"https://doi.org/10.2996/KMJ44108","url":null,"abstract":"The Hurwitz metric was recently defined by Minda by considering a variational problem that involves holomorphic maps from the disc that are globally injective at the origin. In this note, sharp boundary estimates for this metric are obtained on $C^2$-smooth planar domains and as a consequence, it is shown that it is uniformly comparable with the Caratheodory and Kobayashi metrics on such domains. In addition, estimates for the generalized curvatures of this metric are also given.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46018468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A degenerating family of Riemann surfaces over a Riemann surface gives us a monodromy representation, which is a homomorphism from the fundamental group of a punctured surface to the mapping class group. We show that, given such a homomorphism, if its image is finite, then there exists an (isotrivial) degenerating family of Riemann surfaces whose monodromy representation coincides with it. Moreover, we discuss the special sections of such a degenerating family.
{"title":"Degenerating families with finite monodromy groups","authors":"T. Okuda","doi":"10.2996/KMJ44101","DOIUrl":"https://doi.org/10.2996/KMJ44101","url":null,"abstract":"A degenerating family of Riemann surfaces over a Riemann surface gives us a monodromy representation, which is a homomorphism from the fundamental group of a punctured surface to the mapping class group. We show that, given such a homomorphism, if its image is finite, then there exists an (isotrivial) degenerating family of Riemann surfaces whose monodromy representation coincides with it. Moreover, we discuss the special sections of such a degenerating family.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48889343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present paper, we prove that, for an odd prime number $p$ and a positive integer $g$ such that $g-1$ is divisible by $p$, there exists a Tango curve of genus $g$ in characteristic $p$.
{"title":"A note on the existence of Tango curves","authors":"Yuichiro Hoshi","doi":"10.2996/KMJ44105","DOIUrl":"https://doi.org/10.2996/KMJ44105","url":null,"abstract":"In the present paper, we prove that, for an odd prime number $p$ and a positive integer $g$ such that $g-1$ is divisible by $p$, there exists a Tango curve of genus $g$ in characteristic $p$.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42771893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On compact almost complex manifolds, we defined two parabolic flows, which are called the almost Hermitian flow and the almost Hermitian curvature flow in [3]. We show that the uniform equivalence between almost Hermitian metrics and the solution to the almost Hermitian flow by using the method in [6]. This uniform equivalence holds for the almost Hermitian curvature flow as well.
{"title":"Uniform equivalence between almost Hermitian metrics and the solution to the almost Hermitian flow","authors":"Masaya Kawamura","doi":"10.2996/KMJ44102","DOIUrl":"https://doi.org/10.2996/KMJ44102","url":null,"abstract":"On compact almost complex manifolds, we defined two parabolic flows, which are called the almost Hermitian flow and the almost Hermitian curvature flow in [3]. We show that the uniform equivalence between almost Hermitian metrics and the solution to the almost Hermitian flow by using the method in [6]. This uniform equivalence holds for the almost Hermitian curvature flow as well.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45040024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let f(z, z̄) be a convenient Newton non-degenerate mixed polynomial with strongly polar nonnegative mixed weighted homogeneous face functions. We consider a convenient regular simplicial cone subdivision Σ∗ which is admissible for f and take the toric modification π̂ : X → C associated with Σ∗. We show that the toric modification resolves topologically the singularity of the mixed hypersurface germ defined by f(z, z̄) under the Assumption(*) (Theorem 32). This result is an extension of the first part of Theorem 11 ([4]) by M. Oka, which studies strongly polar positive cases, to strongly polar non-negative cases. We also consider some typical examples (§9).
{"title":"Resolutions of Newton non-degenerate mixed polynomials of strongly polar non-negative mixed weighted homogeneous face type","authors":"Sachiko Saito, Kosei Takashimizu","doi":"10.2996/kmj/kmj44304","DOIUrl":"https://doi.org/10.2996/kmj/kmj44304","url":null,"abstract":"Let f(z, z̄) be a convenient Newton non-degenerate mixed polynomial with strongly polar nonnegative mixed weighted homogeneous face functions. We consider a convenient regular simplicial cone subdivision Σ∗ which is admissible for f and take the toric modification π̂ : X → C associated with Σ∗. We show that the toric modification resolves topologically the singularity of the mixed hypersurface germ defined by f(z, z̄) under the Assumption(*) (Theorem 32). This result is an extension of the first part of Theorem 11 ([4]) by M. Oka, which studies strongly polar positive cases, to strongly polar non-negative cases. We also consider some typical examples (§9).","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45926734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let x be a complex number which has a positive real part, and w_1,...,w_N be positive rational numbers. We write w^s zeta_N (s, x | w_1,...,w_N) as a finite linear combination of the Hurwitz zeta function over Q(x), where zeta_N (s,x |w_1,...,w_N) is the Barnes zeta function and w is a positive rational number explicitly determined by w_1,...,w_N. Furthermore, in the case that x is a positive rational number, we give an explicit formula for the values at non-positive integers for higher order derivatives of the Barnes zeta function involving the generalized Stieltjes constants and the values at positive integers of the Riemann zeta function. At the end of the paper, we give some tables of numerical examples.
{"title":"On values of the higher derivatives of the Barnes zeta function at non-positive integers","authors":"Shin Sakane, Miho Aoki","doi":"10.2996/kmj/kmj45105","DOIUrl":"https://doi.org/10.2996/kmj/kmj45105","url":null,"abstract":"Let x be a complex number which has a positive real part, and w_1,...,w_N be positive rational numbers. We write w^s zeta_N (s, x | w_1,...,w_N) as a finite linear combination of the Hurwitz zeta function over Q(x), where zeta_N (s,x |w_1,...,w_N) is the Barnes zeta function and w is a positive rational number explicitly determined by w_1,...,w_N. Furthermore, in the case that x is a positive rational number, we give an explicit formula for the values at non-positive integers for higher order derivatives of the Barnes zeta function involving the generalized Stieltjes constants and the values at positive integers of the Riemann zeta function. At the end of the paper, we give some tables of numerical examples.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41554818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. García‐Río, A. Haji-Badali, R. Mariño-Villar, M. E. Vázquez‐Abal
{"title":"Four-dimensional homogeneous manifolds satisfying some Einstein-like conditions","authors":"E. García‐Río, A. Haji-Badali, R. Mariño-Villar, M. E. Vázquez‐Abal","doi":"10.2996/kmj/1605063625","DOIUrl":"https://doi.org/10.2996/kmj/1605063625","url":null,"abstract":"","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48099123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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