Vol. 7, No. 9, 2013

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Chow quotients of toric varieties as moduli of stable log maps

Qile Chen and Matthew Satriano

Vol. 7 (2013), No. 9, 2313–2329
Abstract

Let $X$ be a projective normal toric variety and ${T}_{0}$ a rank-$1$ subtorus of the defining torus $T$ of $X$. We show that the normalization of the Chow quotient $X∕∕{T}_{0}$, in the sense of Kapranov, Sturmfels, and Zelevinsky, coarsely represents the moduli space of stable log maps to $X$ with discrete data given by ${T}_{0}\subset X$. We also obtain similar results when ${T}_{0}\to T$ is a homomorphism that is not necessarily an embedding.

Keywords
toric, Kontsevich, stable log map, Chow quotient
Primary: 14H10
Secondary: 14N35