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.

Theta-regularity of curves and Brill–Noether loci / L. Lombardi, W. Niu. - In: MATHEMATICAL RESEARCH LETTERS. - ISSN 1073-2780. - 23:6(2016), pp. 1761-1787. [10.4310/MRL.2016.v23.n6.a9]

Theta-regularity of curves and Brill–Noether loci

L. Lombardi;
2016

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.
abelian varieties, theta-regularity, Brill-Noether curves
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/638656
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