On the birational geometry of the universal Picard variety

Details On the birational geometry of the universal Picard variety On the birational geometry of the universal Picard variety

2010-06-03

arxiv.org/abs/1006.0722v7

Int Math Res Notices (2012) Vol. 2012, No. 4, 740--780

Mathematics

Algebraic Geometry

34 pages, 1 figure, final version (to appear in IMRN)

Scientific paper

10.1093/imrn/rnr045

We compute the Kodaira dimension of the universal Picard variety P_{d,g}
parameterizing line bundles of degree d on curves of genus g under the
assumption that (d-g+1,2g-2)=1. We also give partial results for arbitrary
degrees d and we investigate for which degrees the universal Picard varieties
are birational.

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