Chow Quotients of Toric Varieties as Moduli of Stable Log Maps

2012/01/17 by Qile Chen, Matthew Satriano, Chen, Qile +1
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1201.3406

openalex publication_date 2012/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a projective normal toric variety and T₀ a rank one subtorus of the defining torus of X. We show that the normalization of the Chow quotient X//T₀, in the sense of Kapranov-Sturmfels-Zelevinsky, coarsely represents the moduli space of stable log maps to X with discrete data given by T₀⊂ X.

Citations

• The Evaluation Space of Logarithmic Stable Maps

Related

• Logarithmic stable toric varieties and their moduli
• What is a stable log map?
• Equations for Chow and Hilbert Quotients
• The moduli stack of affine stable toric varieties
• Toric Degenerations of GIT Quotients, Chow Quotients, and M_0,n