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Algebra Seminar

Date:
Location:
POT 745
Speaker(s) / Presenter(s):
Ashwin Deopurkar

Theta characteristics and the Weil pairing on degenerate curves

Abstract:  Often degenerate curves play a crucial role in our understanding of a generic smooth curve. The classical theory of limit linear series developed by Griffiths and Harris studies deformation of a line bundle on a smooth curve to a degenerate curve of compact type.  They used to  this method to prove the Brill-Noether theorem. A totally different proof was given by Cools, Draisma, Payne, and Robeva using degenerate curves of non-compact type. The theory of limit linear series for such curves takes shape of metric graphs and divisors on them. After explaining this interplay of tropical geometry and algebraic geometry, I'd talk about specilizations of theta characteristics and the Weil pairing.