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

Calabi–Yau structure and Bargmann type transformation on the Cayley projective plane Cayley投影平面上的Calabi-Yau结构和Bargmann型变换

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2021-01-19 DOI: 10.2969/jmsj/86638663

Kurando Baba, Kenro Furutani

{"title":"Calabi–Yau structure and Bargmann type transformation on the Cayley projective plane","authors":"Kurando Baba, Kenro Furutani","doi":"10.2969/jmsj/86638663","DOIUrl":"https://doi.org/10.2969/jmsj/86638663","url":null,"abstract":"Our purposes are to show the existence of a Calabi-Yau structure on the punctured cotangent bundle T ∗ 0 (P 2 O) of the Cayley projective plane P O and to construct a Bargmann type transformation between the L2-space on P 2 O and a space of holomorphic functions on T ∗ 0 (P 2 O), which corresponds to the Fock space in the case of the original Bargmann transformation. A Kähler structure on T ∗ 0 (P 2 O) was shown by identifying it with a quadrics in the complex space C{0} and the natural symplectic form of the cotangent bundle T ∗ 0 (P 2 O) is expressed as a Kähler form. Our method to construct the transformation is the pairing of polarizations, one is the natural Lagrangian foliation given by the projection map q : T ∗ 0 (P 2 O) −→ P O and the positive complex polarization defined by the Kähler structure. The transformation gives a quantization of the geodesic flow in terms of one parameter group of elliptic Fourier integral operators whose canonical relations are defined by the graph of the geodesic flow action at each time. It turn out that for the Cayley projective plane the results are not same with other cases of the original Bargmann transformation for Euclidean space, spheres and other projective spaces.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46330968","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

$C^{m}$ semialgebraic sections over the plane 平面上的$C^{m}$半代数截面

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2021-01-16 DOI: 10.2969/jmsj/86258625

C. Fefferman, Garving K. Luli

引用次数: 6

Varieties of minimal rational tangents of unbendable rational curves subordinate to contact structures 接触结构下不可展有理曲线的最小有理切线的多样性

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2021-01-14 DOI: 10.2969/JMSJ/85868586

Jun-Muk Hwang

{"title":"Varieties of minimal rational tangents of unbendable rational curves subordinate to contact structures","authors":"Jun-Muk Hwang","doi":"10.2969/JMSJ/85868586","DOIUrl":"https://doi.org/10.2969/JMSJ/85868586","url":null,"abstract":"A nonsingular rational curve $C$ in a complex manifold $X$ whose normal bundle is isomorphic to $${mathcal O}_{{mathbb P}^1}(1)^{oplus p} oplus {mathcal O}_{{mathbb P}^1}^{oplus q}$$ for some nonnegative integers $p$ and $q$ is called an unbendable rational curve on $X$. Associated with it is the variety of minimal rational tangents (VMRT) at a point $x in C,$ which is the germ of submanifolds ${mathcal C}^C_x subset {mathbb P} T_x X$ consisting of tangent directions of small deformations of $C$ fixing $x$. Assuming that there exists a distribution $D subset TX$ such that all small deformations of $C$ are tangent to $D$, one asks what kind of submanifolds of projective space can be realized as the VMRT ${mathcal C}^C_x subset {mathbb P} D_x$. When $D subset TX$ is a contact distribution, a well-known necessary condition is that ${mathcal C}_x^C$ should be Legendrian with respect to the induced contact structure on ${mathbb P} D_x$. We prove that this is also a sufficient condition: we construct a complex manifold $X$ with a contact structure $D subset TX$ and an unbendable rational curve $C subset X$ such that all small deformations of $C$ are tangent to $D$ and the VMRT ${mathcal C}^C_x subset {mathbb P} D_x$ at some point $xin C$ is projectively isomorphic to an arbitrarily given Legendrian submanifold. Our construction uses the geometry of contact lines on the Heisenberg group and a technical ingredient is the symplectic geometry of distributions the study of which has originated from geometric control theory.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43249400","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: 2

Stochastic integrals and Brownian motion on abstract nilpotent Lie groups 抽象幂零李群上的随机积分和布朗运动

IF 0.7 4区数学

Journal of the Mathematical Society of Japan Pub Date : 2021-01-12 DOI: 10.2969/jmsj/84678467

T. Melcher

引用次数: 0

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":null,"pages":null},"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