Non-normal abelian covers

2012/03/20 by Valery Alexeev, Rita Pardini · 5 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation

paper · pdf · doi:10.1112/s0010437x11007482

Abstract

Abstract An abelian cover is a finite morphism X → Y of varieties which is the quotient map for a generically faithful action of a finite abelian group G . Abelian covers with Y smooth and X normal were studied in [R. Pardini, Abelian covers of algebraic varieties , J. Reine Angew. Math. 417 (1991), 191–213; MR 1103912(92g:14012) ]. Here we study the non-normal case, assuming that X and Y are S 2 varieties that have at worst normal crossings outside a subset of codimension greater than or equal to two. Special attention is paid to the case of ℤ r 2 -covers of surfaces, which is used in [V. Alexeev and R. Pardini, Explicit compactifications of moduli spaces of Campedelli and Burniat surfaces , Preprint (2009), math.AG/arXiv:0901.4431] to construct explicitly compactifications of some components of the moduli space of surfaces of general type.

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