Stack of S3-covers
Abstract
The aim of this paper is to study the geometry of the stack of S3-covers. We show that it has two irreducible components ZS3 and Z2 meeting in a "degenerate" point \0\, Z2-\0\ BGL2, while (ZS3-\0\), which contains B S3 as open substack, is a smooth and universally closed algebraic stack. More precisely we show that ZS3-\0\[X/GL2], where X is an explicit smooth non degenerate projective surface inside P7 intersection of five quadrics. All these results are based on the description of certain families of S3-covers in terms of "building data".
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