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

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arxiv 2310.18623 v3 pith:3QN764YH submitted 2023-10-28 math.AG

Gianluca Occhetta , Eleonora A. Romano , Luis E. Solá Conde , Jaros{l}aw A. Wiśniewski This is my paper · ORCID
classification math.AG
keywords chowquotientsvarietyquotientactionactionsarisesassociated
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Mixed Eulerian numbers and beyond

    math.AG 2025-02 accept novelty 8.0 of 10

    First explicit formula for mixed Eulerian numbers, and proof that matroidal mixed Eulerian numbers determine Derksen's G-invariant.

  2. Canonical blow-ups of Grassmannians I: How canonical is a Kausz compactification?

    math.AG 2024-11 conditional novelty 7.0 of 10

    Kausz compactifications and spaces of complete collineations are unified as total space and base of a single torus-equivariant blow-up family over Grassmannians.

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