Theta-regularity of curves and Brill-Noether loci

Abstract

We provide a bound on the $\Theta$-regularity of an arbitrary reduced and irreducible curve embedded in a polarized abelian variety in terms of its degree and codimension. This is an "abelian" version of Gruson-Lazarsfeld-Peskine's bound on the Castelnuovo--Mumford regularity of a non-degenerate curve embedded in a projective space. As an application, we provide a Castelnuovo type bound for the genus of a curve in a (non necessarily principally) polarized abelian variety. Finally, we bound the $\Theta$-regularity of a class of higher dimensional subvarieties in Jacobian varieties, i.e. the Brill-Noether loci associated to a Petri general curve, extending earlier work of Pareschi-Popa.

19 pages. Sections 2 and 3 replace our older preprint arXiv:1209.4404. The material in sections 4 and 5 is new

References in corpus (1)

• Regularity on abelian varieties III: relationship with Generic Vanishing and applications

Cited by in corpus (1)

• Castelnuovo-Mumford Regularity and GV-Sheaves on Irregular Varieties