Mathematics Seminar Date: Thursday, 26 October 2023 Time: 3:30 - 4:30 PM Venue: Lecture Hall 06 Weil pairing on twisted curves Ashwin Deopurkar Columbia University. 26-10-23 Abstract Let C be a smooth, proper curve over an algebraically closed field of characteristic different from two. The Weil pairing on C is an alternating, perfect pairing on Pic(C)[2]. As C varies in the moduli M_g of smooth, genus g curves, this gives a pairing on the two torsion of the relative Picard group. In our work, we extend this pairing on so called twisted curves which give an alternative compactification of M_g that is more suitable in our context. Moreover, we relate the Weil pairing on a twisted curve to a certain combinatorial integration-homology pairing on its dual graph.
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