Algebraic Geometry in String Theory Seminar

Speaker: Alessandro Chiodo, IMJ-Paris Rive Gauche (Jussieu)

Title: The logarithmic double ramification locus

Abstract: Given a family of smooth curves C -> S with a line bundle L on C, it is natural to study the locus of points x in S where L_x is trivial on C_x. When the family is stable, the definition can be extended, not directly on the base scheme S, but more naturally on a (logarithmic) blow-up S’ of S. The problem is in many ways analogue to the problem of defining a Néron model on the moduli space of stable curves (instead of a DVR). Over the past years, David Holmes and his collaborators pioneered a new approach on a logarithmic modification of the entire moduli space of curves. In this talk, we determine this logarithmic double ramification cycle and several variants and alternative presentations of it (work in collaboration with David Holmes).