The classification of universal Jacobians over the moduli space of curves
49 citations recorded by the source corpus.
We carry out a complete birational classification of the degree g universal Jacobian P_g over the moduli space of curves, highlighting the transition cases g=10, 11. The universal Jacobian is unirational when g 11, the variety P_g has Kodaira dimension 3g-3, that is, the maximum allowed by Iitaka's easy addition formula for fibre spaces. In particular, we disprove the expectation that P_g and M_g have the same Kodaira dimension for all genera.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5118825108363c27d685b0e02212707633a9478d
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Alternate Compactifications of Moduli Spaces of Curves (2010, background): “These include rationality, unirationality and rational connectedness of Mg,n [SB87, SB89, Kat91, Kat96, MM83, Ver05, BV05], complete subvarieties of Mg,n [Dia84, FvdG04, GK08], birational geometry of Prym varieties [Don84, Cat83, Ver84, Ver08, Kat94, Dol08, ILGS09, FL10], Kodaira dimension of Mg,n f”