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