Chow quotients of toric varieties as moduli of stable log maps

Chen, Qile; Satriano, Matthew

doi:10.2140/ant.2013.7.2313

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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

DOI: 10.2140/ant.2013.7.2313

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

Mathematical Subject Classification 2010

Primary: 14H10

Secondary: 14N35

Milestones

Received: 22 October 2012

Revised: 4 February 2013

Accepted: 12 March 2013

Published: 18 December 2013

Authors

Qile Chen
Department of Mathematics Columbia University 2990 Broadway New York, NY 10027 United States

Matthew Satriano
Department of Mathematics University of Michigan 2074 East Hall Ann Arbor, MI 48109 United States

Vol. 7, No. 9, 2013