Cox rings and symplectic quotient singularities with torus action

2018/07/30 by Grab, Maksymilian
#14C20 #14E15 #14L24 #14L30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.11438

Abstract

We develop a method of finding a Cox ring of a crepant resolution of a quotient singularity with a torus action and apply it to examples of symplectic quotient singularities in dimension 4. In addition we obtain a bound on the degrees of homogeneous generators of the Cox ring in a more general setup, based on the multigraded Castelnuovo-Mumford regularity and Kawamata-Viehweg vanishing.

Related

• Cox rings of some symplectic resolutions of quotient singularities
• Cox rings of minimal resolutions of surface quotient singularities
• Crepant resolutions of 3-dimensional quotient singularities via Cox\n rings
• Log terminal singularities, platonic tuples and iteration of Cox rings
• Uniqueness of crepant resolutions and symplectic singularities