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arXiv · 2503.19663

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

Gianluca Occhetta·Luis E. Solá Conde
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Abstract

In this paper we study the Chow quotient ${\mathcal C}X$ 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 ${\mathcal C}X$ parametrizing reducible torus-invariant cycles is a simple normal crossing divisor, we compute the Nef and Mori cones of ${\mathcal C}X$, and its anticanonical divisor.

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Gianluca Occhetta, Luis E. Solá Conde. 2025-03-25. Chow quotients of ${\mathbb C}^*$-actions on convex varieties. https://arxiv.org/abs/2503.19663

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