Moduli of products of stable varieties
Algebraic Geometry
2019-02-20 v1
Abstract
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 \'etale, 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.
Keywords
Cite
@article{arxiv.1206.0438,
title = {Moduli of products of stable varieties},
author = {Bhargav Bhatt and Wei Ho and Zsolt Patakfalvi and Christian Schnell},
journal= {arXiv preprint arXiv:1206.0438},
year = {2019}
}
Comments
26 pages, suggestions and comments are welcomed