Journal of the Mathematical Society of Japan最新文献_第9页

On 3-2-1 values of finite multiple harmonic $q$-series at roots of unity 关于单位根上有限多次调和$q$-级数的3-2-1值

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2021-01-10 DOI: 10.2969/jmsj/86238623

Khodabakhsh Hessami Pilehrood, T. H. Pilehrood, R. Tauraso

引用次数: 1

On higher dimensional extremal varieties of general type 关于一般型的高维极值变体

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2021-01-09 DOI: 10.2969/jmsj/88668866

Purnaprajna Bangere, J. Chen, F. Gallego

{"title":"On higher dimensional extremal varieties of general type","authors":"Purnaprajna Bangere, J. Chen, F. Gallego","doi":"10.2969/jmsj/88668866","DOIUrl":"https://doi.org/10.2969/jmsj/88668866","url":null,"abstract":"Relations among fundamental invariants play an important role in algebraic geometry. It is known that an n-dimensional variety of general type with nef canonical divisor and canonical singularities, whose image Y under the canonical map is of maximal dimension, satisfies K X ≥ 2(pg − n). We investigate the very interesting extremal situation K X = 2(pg−n), which appears in a number of geometric situations. Since these extremal varieties are natural higher dimensional analogues of Horikawa surfaces, we name them Horikawa varieties. These varieties have been previously dealt with in the works of Fujita [Fuj83] and Kobayashi [Kob92]. We carry out further studies of Horikawa varieties, proving new results on various geometric and topological issues concerning them. In particular, we prove that the geometric genus of those Horikawa varieties whose image under the canonical map is singular is bounded. We give an analogous result for polarized hyperelliptic subcanonical varieties, in particular, for polarized Calabi-Yau and Fano varieties. The pleasing numerology that emerges puts Horikawa’s result on surfaces in a broader perspective. We obtain a structure theorem for Horikawa varieties and explore their pluriregularity. We use this to prove optimal results on projective normality of pluricanonical linear systems. We study the fundamental groups of Horikawa varieties, showing that they are simply connected, even if Y is singular. We also prove results on deformations of Horikawa varieties, whose implications on the moduli space make them the higher dimensional analogue of curves of genus 2.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49188668","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}

引用次数: 3

On the multicanonical systems of quasi-elliptic surfaces 拟椭圆曲面的多谐系统

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2021-01-01 DOI: 10.2969/jmsj/85058505

Natsuo Saito, Bstract

引用次数: 0

Diophantine approximation in number fields and geometry of products of symmetric spaces 数域的丢番图近似与对称空间积的几何

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2021-01-01 DOI: 10.2969/JMSJ/81358135

T. Hattori

引用次数: 2

On the Milnor fibration for $f(boldsymbol{z}) bar{g}(boldsymbol{z})$ II 关于$f(boldsymbol{z}) bar{g}(boldsymbol{z})$ II的Milnor振动

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2021-01-01 DOI: 10.2969/JMSJ/83328332

M. Oka

引用次数: 2

The hypergeometric function, the confluent hypergeometric function and WKB solutions 超几何函数、合流超几何函数和WKB解

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2021-01-01 DOI: 10.2969/jmsj/84528452

T. Aoki, Toshinori Takahashi, M. Tanda

引用次数: 2

Optimal singularities of initial functions for solvability of a semilinear parabolic system 一类半线性抛物型系统可解性的初始函数的最优奇异性

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2020-12-10 DOI: 10.2969/jmsj/86058605

Y. Fujishima, Kazuhiro Ishige

引用次数: 4

Default functions and Liouville type theorems based on symmetric diffusions 基于对称扩散的默认函数和Liouville型定理

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2020-12-01 DOI: 10.2969/jmsj/82398239

A. Atsuji

{"title":"Default functions and Liouville type theorems based on symmetric diffusions","authors":"A. Atsuji","doi":"10.2969/jmsj/82398239","DOIUrl":"https://doi.org/10.2969/jmsj/82398239","url":null,"abstract":"Default functions appear when one discusses conditions which ensure that a local martingale is a true martingale. We show vanishing of default functions of Dirichlet processes enables us to obtain Liouville type theorems for subharmonic functions and holomorphic maps. Default functions were introduced in [7] and it is known that vanishing of the default function of a local martingale implies that it is a true martingale. Positivity of the default function then indicates the singularity of local martingale. Such local martingales are called strictly local martingales. Recently strictly local martingales are playing important roles in the theory of financial bubbles (cf. [19]), so the notion of default function becomes important in mathematical finance area. We consider them in a different context. In mathematical analysis of subharmonic functions it is classical and natural to consider the functions along Brownian motions. A stochastic process derived from a subharmonic function composed with Brownian motion is a local submartingale. Then if we know that the process is a true submartingale, which follows from vanishing of the default function of the submartingale, it effects simpleness and clearness in analysis of subharmonic functions. In this paper we intend to show that this probabilistic notion plays effective roles in some analysis such as L-Liouville type theorems of subharmonic functions and Liouville type theorems for functions satisfying some nonlinear differential inequalities. It covers and extends the precedent results about L-Liouville theorem for subharmonic functions 2000 Mathematics Subject Classification. Primary 31C05; Secondary 58J65.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43576089","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}

引用次数: 0

Effective Łojasiewicz gradient inequality for Nash functions with application to finite determinacy of germs 有效的Łojasiewicz梯度不等式纳什函数及其在细菌有限确定性中的应用

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2020-12-01 DOI: 10.2969/jmsj/83378337

Beata Osińska-Ulrych, Grzegorz Skalski, S. Spodzieja

引用次数: 0

Comparison geometry of manifolds with boundary under lower $N$-weighted Ricci curvature bounds with $varepsilon$-range 具有$varepsilon$范围的较低$N$加权Ricci曲率边界下具有边界的流形的几何比较

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2020-11-07 DOI: 10.2969/jmsj/87278727

K. Kuwae, Y. Sakurai

引用次数: 0