Chow quotients of \mathbb C^*-actions on convex varieties

2025/03/25 by Occhetta, Gianluca, Conde, Luis E. Solá
#14J45 #14L24 #14M17 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14L30 #Secondary 14E30

paper · doi:10.48550/arxiv.2503.19663

Abstract

In this paper we study the Chow quotient \mathcal CX of a convex variety X of Picard number one by the action of a one dimensional torus having no non-trivial finite isotropy. Examples of these actions can be found in the rational homogeneous framework. We prove that the subvariety of \mathcal CX parametrizing reducible torus-invariant cycles is a simple normal crossing divisor, we compute the Nef and Mori cones of \mathcal CX, and its anticanonical divisor.

Related

• Chow quotients of ℂ^*-actions
• Characterizing rational homogeneous spaces via ℂ^*-actions
• Topological Aspects of Chow Quotients
• The cone of effective one-cycles of certain G-varieties
• Inversion maps and torus actions on rational homogeneous varieties