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.
G. Bini, C. Fontanari, F. Viviani (2012). On the Birational Geometry of the Universal Picard Variety. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2012(4), 740-780 [10.1093/imrn/rnr045].
On the Birational Geometry of the Universal Picard Variety
G. Bini;
2012-01-01
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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