Moduli of products of stable varieties

Bhargav Bhatt, Wei Ho, Zsolt Patakfalvi, Christian Schnell

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10 Scopus citations


We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined morphism from the product of moduli spaces of stable varieties to the moduli space of a product of stable varieties; (b) this map is always finite étale; and (c) this map very often is an isomorphism. Our results generalize and complete the work of Van Opstall in dimension 1. The local results rely on a study of the cotangent complex using some derived algebro-geometric methods, while the global ones use some differential-geometric input.

Original languageEnglish (US)
Pages (from-to)2036-2070
Number of pages35
JournalCompositio Mathematica
Issue number12
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


  • cotangent complex
  • deformation theory
  • derived algebraic geometry
  • moduli spaces
  • stable varieties
  • stable vector bundles


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