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arXiv · 1102.4184

Non-normal abelian covers

Valery Alexeev·Rita Pardini
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Abstract

An abelian cover is a finite morphism $X\to Y$ 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 \cite{Pardini_AbelianCovers}. 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 $\ge 2$. Special attention is paid to the case of $\Z_2^r$-covers of surfaces, which is used in arxiv:0901.4431 to construct explicitly compactifications of some components of the moduli space of surfaces of general type.

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Valery Alexeev, Rita Pardini. 2011-10-10. Non-normal abelian covers. https://doi.org/10.1112/s0010437x11007482

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