Tautological relations via the Abel--Jacobi map

Dmitry Zakharov, September 10th, 2013

Given a curve with marked points and integer weights on the markings, we consider the
corresponding divisor. This defines an Abel--Jacobi map from the moduli space of
marked curves to the universal Jacobian variety. This map extends to the space of curves
of compact type. 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.