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

Let X be a projective normal toric variety and T0 a rank-1 subtorus of the defining torus T of X. We show that the normalization of the Chow quotient X ∕∕ T0, in the sense of Kapranov, Sturmfels, and Zelevinsky, coarsely represents the moduli space of stable log maps to X with discrete data given by T0 X. We also obtain similar results when T0 T is a homomorphism that is not necessarily an embedding.

toric, Kontsevich, stable log map, Chow quotient
Mathematical Subject Classification 2010
Primary: 14H10
Secondary: 14N35
Received: 22 October 2012
Revised: 4 February 2013
Accepted: 12 March 2013
Published: 18 December 2013
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