Jay Kopper : Some problems in extending Brill-Noether theory from the classical case: the sky is the limit linear series

Posted by John Kopper , part of the Graduate Algebraic Geometry Seminar.

At

Oct. 11, 2017, 1 p.m.

In

SEO 712

Abstract

Classical Brill-Noether theory asks how many global sections a line bundle on a (general) smooth curve can have. This was solved (completely, in some sense) by Griffiths-Harris several decades ago. A number of natural generalizations remain open: what if we ask about (semistable) vector bundles instead of line bundles? What if our curves are not Brill-Noether general but nonetheless lie in an interesting family? In this talk I will pose but fail to answer some of these very interesting questions.