Picard bundles and brill–noether loci in the compactified Jacobian of a nodal curve

Bhosle, Usha N. ; Parameswaran, A. J. (2013) Picard bundles and brill–noether loci in the compactified Jacobian of a nodal curve International Mathematics Research Notices, 2014 (15). pp. 4241-4290. ISSN 1073-7928

Full text not available from this repository.

Official URL: https://academic.oup.com/imrn/article-abstract/201...

Related URL: http://dx.doi.org/10.1093/imrn/rnt069

Abstract

Let Xk denote an irreducible projective nodal curve with k nodes and of genus g(k). We prove a generalization of the classical Poincaré formula to the compactified Jacobian J̅0k the moduli space of torsion-free sheaves of rank 1 and degree 0 on Xk. We apply it to show that the Brill–Noether loci are nonempty if the Brill–Noether number is nonnegative. We prove that for d≥2g(Xk), the Picard bundle on J̅0k is stable but not ample, unlike in the case of a smooth curve. However, for the pullback of the Picard bundle to the desingularization of J̅0k, the restriction to a general complete intersection subvariety of codimension k is ample. We use this to show that the Brill–Noether loci are connected if the Brill–Noether number is bigger than k. We prove that the Picard bundle is semistable for d=2g(Xk)−1.

Item Type:Article
Source:Copyright of this article belongs to Oxford University Press.
ID Code:112226
Deposited On:23 Jan 2018 12:10
Last Modified:23 Jan 2018 12:10

Repository Staff Only: item control page