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Research of new developments in moduli spaces and integrable systems

模空间与可积系统研究新进展

基本信息

批准号：
16340009
负责人：
SAITO Masa-hiko
金额：
$ 10.37万
依托单位：
Kobe University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

项目摘要

In the present research, Inaba, Iwasaki and Saito constructed the moduli space of stable parabolic connections of rank 2 over the projective line with at most n-regular singular points and its natural compactification, and showed the smoothness of the moduli space. Moreover, constructing the moduli space of the representations of the fundamental group of the complement of the n-points in projective plane, we showed that Riemann-Hilbert correspondence from the moduli space of connections to the moduli space of the representations is a surjective proper bimeromorphic morphism. This result implies that the non-linear differential equations coming from isomonodromic deformations of connections have Painleve property. Recently Inaba succeeded in generalizing this result to the case of stable parabolic connections with at most regular singularities of any rank over any smooth algebraic curve. We expect further to obtain the same result in the case of connections with irregular singular point … More s. Noumi and Yamada gave a geometric description of elliptic difference Painleve equations with Ohta, Masuda, Kajiwara, and construct the elliptic hypergeometric solutions and its degeneration.By using the algebro-geometric construction of Painleve VI equations and applying the Riemann-Hilbert correspondence to ergotic theory of algebraic surfaces, Iwasaki and Uehara showed that the dynamics of almost loops of non-linear monodromy of Painleve VI equation are chaotic. Hosono and Doran determined the differential equation of the period integrals of certain class of Calabi-Yau hypersurfaces by oscillatory integrals. Moreover solving the Stokes phenomena associated to the integral, they observed a natural understanding from the view point of Mirror symmetry. Yoshioka and Hiraku Nakajima proved the Nekrasov conjecture for the instanton numbers. Moreover with Lotha Gottsche, they obtained a wall-crossing formula for Donaldson invariants for the rational surfaces, and extend the results. Fukaya, Ono, Ohta, Oh, are completing a big book of Floer theory of Lagrangian submanifolds. Less

Inaba，Iwasaki和Saito构造了至多n-正则奇点的射影直线上秩为2的稳定抛物联络的模空间及其自然紧化，并证明了模空间的光滑性.通过构造射影平面上n点补的基本群的表示的模空间，证明了从联络的模空间到表示的模空间的Riemann-Hilbert对应是满射真双半纯态射.这一结果意味着由节点的等单点变形所形成的非线性微分方程具有Painleve性质。最近稻叶成功地推广这一结果的情况下，稳定的抛物型连接与最经常的奇异性的任何秩在任何光滑的代数曲线。我们期望进一步在具有非正则奇点的联络的情形下得到同样的结果 ...更多信息 S. Noumi和Yamada与Ohta，增田，Kajiwara等人给出了椭圆型差分Painleve方程的几何描述，构造了椭圆型超几何解及其退化，Iwasaki和Uehara利用Painleve VI方程的代数几何构造，将Riemann-Hilbert对应应用于代数曲面的遍历理论，证明了Painleve VI方程的非线性单值几乎环动力学是混沌的. Hosono和Doran利用振荡积分确定了一类Calabi-Yau超曲面的周期积分微分方程。此外，解决斯托克斯现象相关的积分，他们观察到一个自然的理解，从观点的镜像对称。Yoshioka和Hiraku Nakajima证明了Nekrasov猜想。此外，他们与Lotha Gottsche一起得到了有理曲面的唐纳森不变量的一个跨壁公式，推广了已有的结果。福谷，小野，太田，哦，正在完成一本大书的弗洛尔理论的拉格朗日子流形。少