Chow quotients of ℂ^*-actions

2023/10/28 by Occhetta, Gianluca, Romano, Eleonora A., Conde, Luis E. Solá +1
#14L24 #14M17 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14L30 #Secondary 14E30

paper · doi:10.48550/arxiv.2310.18623

Abstract

Given an action of the one-dimensional torus on a projective variety, the associated Chow quotient arises as a natural parameter space of invariant 1-cycles, which dominates the GIT quotients of the variety. In this paper we explore the relation between the Chow and the GIT quotients of a variety, showing how to construct explicitly the former upon the latter via successive blowups under suitable assumptions. We also discuss conditions for the smoothness of the Chow quotient, and present some examples in which it is singular.

Related

• Chow quotients of \mathbb C^*-actions on convex varieties
• Topological Aspects of Chow Quotients
• Chow quotients of Grassmannian I
• Equations for Chow and Hilbert Quotients
• All the GIT quotients at once