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
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.File | Dimensione | Formato | |
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