Toric hyperkähler varieties and Q-factorial terminalizations

2023/11/26 by Namikawa, Yoshinori
#14 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.15177

Abstract

A toric hyperkähler variety is determined by combinatorial data A and α. Here A is an integer valued matrix and α is a character of an algebraic torus T^d. Y(A, α) is a crepant partial resolution of an affine toric hyperkähler variety Y(A,0). However, Y(A, α) is not generally a Q-factorial terminalization of Y(A,0) even if α is generic. In this article, we realize Y(A,0) as another toric hyperkähler variety Y(A^\sharp, 0) so that Y(A^\sharp, α^\sharp) is a Q-factorialization of Y(A^\sharp, 0) for a generic α^\sharp. As an application, we give a necessary and sufficient condition for Y(A,0) to have a crepant resolution. Moreover, we construct explicitly the universal Poisson deformation of Y(A,0) in terms of A^\sharp.

Related

• Toric Hyperkahler Varieties
• Fibred toric varieties in toric hyperkähler varieties
• Tate resolutions on toric varieties
• Toric Q-Gorenstein Singularities
• Higher K-theory of toric varieties