Logarithmic stable toric varieties and their moduli

Kenneth Ascher, Samouil Molcho

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageEnglish (US)
Pages (from-to)296-319
Number of pages24
JournalAlgebraic Geometry
Issue number3
StatePublished - May 1 2016

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology


  • Chow quotients
  • Log stable maps
  • Stable toric varieties
  • Toric stacks


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