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arXiv · 1412.3766

Logarithmic stable toric varieties and their moduli

Kenneth Ascher·Samouil Molcho
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Abstract

The Chow quotient of a toric variety by a subtorus, as defined by Kapranov-Sturmfels-Zelevinsky, coarsely represents the main component of the moduli space of stable toric varieties with a map to a fixed projective toric variety, as constructed by Alexeev and Brion. We show that, after endowing both spaces with the structure of a logarithmic stack, the resulting spaces are isomorphic. Along the way, we construct the Chow quotient stack and demonstrate several properties that it satisfies.

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Kenneth Ascher, Samouil Molcho. 2014-12-11. Logarithmic stable toric varieties and their moduli. https://arxiv.org/abs/1412.3766

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