We prove that any 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 to the Albanese variety of its Fano surface of lines.

GV-subschemes and their embeddings in principally polarized abelian varieties / L. Lombardi, S. Tirabassi. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 288:11-12(2015 Aug), pp. 1405-1412. [10.1002/mana.201400238]

GV-subschemes and their embeddings in principally polarized abelian varieties

L. Lombardi
Primo
;
2015

Abstract

We prove that any 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 to the Albanese variety of its Fano surface of lines.
Fano surfaces of lines; Fourier-Mukai transforms; Generic vanishing; Minimal cohomology classes
Settore MAT/03 - Geometria
ago-2015
24-feb-2015
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/652306
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