Brill-Noether loci of rank two vector bundles on a general ν-gonal curve

2017/02/03 by Youngook Choi, Choi, Youngook, Flaminio Flamini +3
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1702.00918

Abstract

In this paper we study the Brill Noether locus of rank 2, (semi)stable vector bundles with at least two sections and of suitable degrees on a general ν-gonal curve. We classify its reduced components whose dimensions are at least the corresponding Brill-Noether number. We moreover describe the general member \mathcal F of such components just in terms of extensions of line bundles with suitable \em minimality properties, providing information on the birational geometry of such components as well as on the very-ampleness of \mathcal F.

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