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.