John Kopper : The locus of non-globally generated vector bundles on curves

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

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Sept. 14, 2020, 4:30 p.m.

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Abstract

A general stable vector bundle on a smooth curve is globally generated as soon as its Euler characteristic is greater than its rank. The complement of the locus of globally generated stable bundles thus has positive codimension and describing its geometry is a topic of interest in the higher rank Brill-Noether theory of the curve. In this talk, I will discuss some new results about the dimension and irreducibility of this non-globally generated locus. We are able to compute its dimension in all cases and show that it is irreducible under certain numerical hypotheses. This is joint work with Sayanta Mandal.