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Moduli of products of stable varieties
- Part of
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- Journal:
- Compositio Mathematica / Volume 149 / Issue 12 / December 2013
- Published online by Cambridge University Press:
- 06 September 2013, pp. 2036-2070
- Print publication:
- December 2013
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- Article
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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.
