Subvarieties of Abelian Varieties

By E. Izadi. 2001

65 citations recorded by the source corpus.

We discuss various constructions which allow one to embed a principally polarized abelian variety in the jacobian of a curve. Each of these gives representatives of multiples of the minimal cohomology class for curves which in turn produce subvarieties of higher dimension representing multiples of the minimal class. We then discuss the problem of producing curves representing multiples of the minimal class via deformation-theoretic methods.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/491af04fcaa9612ec1b5afa570d791251113a766

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In Computational Theory and Mathematics

1. Mihnea Cristian Popa
2. Giuseppe Pareschi
3. S. Grushevsky

In Geometry and Topology

1. Mihnea Cristian Popa
2. Giuseppe Pareschi
3. S. Grushevsky
4. C. Schnell
5. Nero Budur

Citations in the corpus

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• Strong generic vanishing and a higher-dimensional Castelnuovo–de Franchis inequality (2008, background): “hic 1-forms, which is the key ingredient in the classical proof on surfaces. Various highly interesting higher-dimensional generalizations of this result do exist in the literature (cf. [Cat], [GL2], [Ra]). Their main thrust is however in a different direction, not directly linked to the holomorphic ”