Let be a projective normal toric variety and a rank- subtorus of the defining torus of . We show that the normalization of the Chow quotient , in the sense of Kapranov, Sturmfels, and Zelevinsky, coarsely represents the moduli space of stable log maps to with discrete data given by . We also obtain similar results when is a homomorphism that is not necessarily an embedding.
Qile Chen. Matthew Satriano. "Chow quotients of toric varieties as moduli of stable log maps." Algebra Number Theory 7 (9) 2313 - 2329, 2013. https://doi.org/10.2140/ant.2013.7.2313