GV-subschemes and their embeddings in principally polarized abelian varieties

Luigi Lombardi; Sofia Tirabassi

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arXiv · 1407.6835

GV-subschemes and their embeddings in principally polarized abelian varieties

Luigi Lombardi·Sofia Tirabassi

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Abstract

We prove that the embedding of a $GV$-subscheme in a principally polarized abelian variety does not factor through any nontrivial isogeny. As an application, we present a new proof of a theorem of Clemens--Griffiths identifying the intermediate Jacobian of a smooth cubic threefold in $\mathbf{P}^4$ to the Albanese variety of its Fano surface of lines.

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Luigi Lombardi, Sofia Tirabassi. 2014-07-25. GV-subschemes and their embeddings in principally polarized abelian varieties. https://arxiv.org/abs/1407.6835

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