Moduli of products of curves

2003/07/08 by Michael van Opstall, van Opstall, Michael
Mathematics · #14J10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J10

paper · pdf · doi:10.48550/arxiv.math/0307094

Revised version simplifies and generalizes some proofs. Typos fixed. 5 pages

arxiv created 2003/11/03 · arxiv updated 2009/12/01

Abstract

This paper studies the moduli space of stable surfaces of general type. The moduli space component containing the moduli point of a product of smooth curves of general type is proved to be the product of the moduli spaces of the curves, unless the curves have the same genus, in which case it is the symmetric product of the moduli space of curves. This result follows from a study of deformation theory of products and the singularities of products of nodal curves (namely that the product of nodal curves has semilogcanonical singularities).

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