Theta-regularity of curves and Brill-Noether loci

2014/10/29 by Lombardi, Luigi, Niu, Wenbo
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1410.8047

Abstract

We provide a bound on the Θ-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 Θ-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.

Related

• Regularity of curves in abelian varieties
• Severi Varieties and Brill-Noether theory of curves on abelian surfaces
• Degrees of Curves in Abelian Varieties
• Seshadri constants and hyperelliptic curves on abelian varieties
• Degeneration of Riemann theta functions and of the Zhang-Kawazumi invariant with applications to a uniform Bogomolov conjecture