We show that the infinitesimal deformations of Brill-Noether loci W-d attached to a smooth non-hyperelliptic curve C are in one-to-one correspondence with the deformations of C. As an application, we prove that if a Jacobian J deforms together with a minimal cohomology class out the Jacobian locus, then J is hyperelliptic. In particular, this provides an evidence toward a conjecture of Debarre on the classification of ppavs carrying a minimal cohomology class.

Deformations of minimal cohomology classes on abelian varieties / L. Lombardi, S. Tirabassi. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 18:4(2016 Aug), pp. 1550066.1-1550066.23. [10.1142/S0219199715500662]

Deformations of minimal cohomology classes on abelian varieties

L. Lombardi
Primo
;
2016-08

Abstract

We show that the infinitesimal deformations of Brill-Noether loci W-d attached to a smooth non-hyperelliptic curve C are in one-to-one correspondence with the deformations of C. As an application, we prove that if a Jacobian J deforms together with a minimal cohomology class out the Jacobian locus, then J is hyperelliptic. In particular, this provides an evidence toward a conjecture of Debarre on the classification of ppavs carrying a minimal cohomology class.
Deformations; minimal cohomology classes; Jacobian;
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/638654
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