Brill–Noether loci of rank 2 vector bundles on a general 𝜈-gonal curve

Choi, Youngook; Flamini, Flaminio; Kim, Seonja

doi:10.1090/proc/14093

Brill–Noether loci of rank 2 vector bundles on a general $\nu$-gonal curve
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by Youngook Choi, Flaminio Flamini and Seonja Kim PDF

Proc. Amer. Math. Soc. 146 (2018), 3233-3248 Request permission

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 $\nu$-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 only in terms of extensions of line bundles with suitable 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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