Chennai Mathematical Institute

Seminars




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.