Orateur
Description
Let C/S be a family of curves, and L on C a line bundle. The double ramification (DR) cycle measures the locus D \subset S over which L is fibrewise trivial. To say the same thing another way, the restriction of L to C \times_S D is a pullback of some line bundle L' on D. Writing Z for the first Chern class of L', we can consider a sequence of cycles DR^0, DR^1, DR^2, ... on the moduli space of curves, defined by taking the product DR^i := Z^i DR. For i=0 this recovers the usual DR cycle, for which a formula can be written by taking the coefficient of r^0 in a certain polynomial in r constructed from Chiodo classes. We will show (under some annoying hypotheses, hopefully to be removed soon) that the cycle DR^i is the coefficient of r^i in the same expression with Chiodo classes. This is joint work with D. Chen, S. Grushevsky, M. Möller, and J. Schmitt.
