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Non-normal abelian covers

Part of: Birational geometry Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  20 March 2012

Valery Alexeev  and
Rita Pardini
Valery Alexeev
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30605, USA (email: [email protected])
Rita Pardini
Affiliation:
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy (email: [email protected])
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Abstract

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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 S2 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 ℤr2-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.

Keywords

coveringsabelian coversnon-normal varietiessurface singularitiesstable surfaces

MSC classification

Secondary: 14E20: Coverings 14J17: Singularities
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 4 , July 2012 , pp. 1051 - 1084
Copyright
Copyright © Foundation Compositio Mathematica 2012

References

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