表題番号:2018K-204 日付:2019/02/08
研究課題インスタントンモジュライの代数幾何学的研究
研究者所属(当時) 資格 氏名
(代表者) 理工学術院 基幹理工学部 講師 大川 領
研究成果概要

 We study moduli of framed sheaves on the projective plane, in particular, generating functions of

integrations over moduli spaces called Nekrasov function. In this year, we try to extend to two cases,

1. other surface, 2. K-theory version.

 In 1. , we computed integrations of other cohomology classes for the minimal resolution of 

A1 singularity. Although we have not checked rigourously, this could implies that we can construct 

Painlvé tau function by Fourier transform of Nekrasov functions. Furthermore, towerd other ADE 

singularities we study finite type quiver varieties as toy models. As a result, we understand that 

general wall-crossing phenomena are reduced to more fundamental cases.

In our case, we study affine quiver varieties, and the minimal resolution of A1 singularity 

seems fundamental. Hence it seems possible to extend previous results to other ADE singularities 

soon. 

 In 2. , we also studied finite type quiver varieties, and also discussed other methods with physicists.