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 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 satisfies.
Original language | English (US) |
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Pages (from-to) | 296-319 |
Number of pages | 24 |
Journal | Algebraic Geometry |
Volume | 3 |
Issue number | 3 |
DOIs | |
State | Published - May 1 2016 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology
Keywords
- Chow quotients
- Log stable maps
- Stable toric varieties
- Toric stacks