Back to Algebraic Geometry Seminar: Fall 2014
Algebraic Geometry Seminar
Date: Tuesday, Oct 28, 2014
Time: 3:30PM - 4:30PM
Location: LCB 225
4:00 pm
Dmitry Zakharov
Courant Institute of Mathematical Sciences, New York University
Title |
The Abel--Jacobi map and relations in the tautological ring |
Abstract |
Given an algebraic curve with marked points and integer weights on the markings, we can consider the corresponding divisor. This defines an Abel–Jacobi map from the moduli space of marked curves of compact type to the universal Jacobian variety. Pulling back relations from the universal Jacobian for various values of the weights gives a plethora of tautological relations on the space of curves of compact type. These relations include those discovered by Faber, Getzler, Belorousski and Pandharipande, and Tavakol, and this method was also used by Hain to compute the double ramification cycle. I will talk about the extension of the Abel–Jacobi map to a larger moduli space of marked curves, the corresponding extended formula for the double ramification cycle, and Pixton’s conjectures about the extensions of these relations to the entire Deligne-Mumford compactification. |
Algebraic Geometry