VERTEX OPERATOR ALGEBRAS AND MODULI SPACES OF ALGEBRAIC CURVES

顶点算子代数和代数曲线的模空间

基本信息

批准号：
15540036
负责人：
ICHIKAWA Takashi
金额：
$ 2.37万
依托单位：
SAGA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

项目摘要

(1)Using arithmetic Schottky-Mumford uniformization theory on algebraic curves, we constructed Teichmuller groupoids in the category of arithmetic geometry. By this construction, we gave a partial answer to Grothendieck's conjecture on the associated Galois representations, and described monodromy representations induced from confbrmal field theory.(2)Extending Ullmo-Zhang's results on Bogomolov's conjecture, we gave a condition that a subvariety of an abelian variety defined over a number field is isomorphic to an abelian variety in terms of Neron-Tate's height functions.(3)We described the structure of Riemann surfaces defined from the monodromy representation of hypergeometric differential equations with purely imaginary exponents (joint work with M.Yoshida).(4)We determined the structure of the class groups and unit groups of algebraic number fields of Kummer type, specifically of quartic Dirichlet fields (joint work with K.Katayama and C.Levesque). Further, we investigated the problem of Hasse concerning power integral basis of the ring of algebraic integers (joint work with Y.Motoda).(5)We defined stochastic holonomy operator and the Chern-Simons integral of some product of gauge invariant Wilson loop observables in the Wiener space setting.(6)We studied Buchsbaum Stanley-Reisner rings with linear resolution and characterized them by their multiplicity. Further, we studied the arithmetical rank and determined it for monomial ideals of deviation two.(7)We studied 4-manifolds having flexible surfaces inside, and showed that a lot of simply connected 4-manifolds not the 4-sphere have flexible surfaces. Further, we introduced an operation to alter any surface in a simply connected 4-manifold into a flexible surface.

（1）我们在代数曲线上使用算术Schottky-Mumford统一理论，我们在算术几何形状类别中构建了Teichmuller群。 By this construction, we gave a partial answer to Grothendieck's conjecture on the associated Galois representations, and described monodromy representations induced from confbrmal field theory.(2)Extending Ullmo-Zhang's results on Bogomolov's conjecture, we gave a condition that a subvariety of an abelian variety defined over a number field is isomorphic to an abelian variety in terms of Neron-Tate's height （3）我们描述了根据具有纯粹虚构指数的超几何微分方程的单层表示所定义的riemann表面的结构（与M.Yoshida的联合工作）。（4）我们确定了类群的结构，以及Kummer类型的代数组和单位组的单位组，特定于Quartic dirichlet dirichelet and k.kats and C.KATSAID和C.KATEASER and C.KATSAIN和C.C.KATEASEN。 Further, we investigated the problem of Hasse concerning power integral basis of the ring of algebraic integers (joint work with Y.Motoda).(5)We defined stochastic holonomy operator and the Chern-Simons integral of some product of gauge invariant Wilson loop observables in the Wiener space setting.(6)We studied Buchsbaum Stanley-Reisner rings with linear resolution and characterized them by their多重性。此外，我们研究了算术等级，并确定了偏差两个的单一理想。（7）我们研究了内部具有柔性表面的4个manifolds，并表明许多简单地连接的4个manifolds，而不是4个球体具有柔性表面。此外，我们引入了一个操作，以将简单连接的4个manifold中的任何表面更改为柔性表面。