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.
On the Birational Geometry of the Universal Picard Variety / G. Bini, C. Fontanari, F. Viviani. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2012:4(2012), pp. 740-780.
On the Birational Geometry of the Universal Picard Variety
G. BiniPrimo
;
2012
Abstract
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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