Abstract

Inside the moduli space of smooth pointed curves, the double-ramification locus is cut out by the condition that the curve admits a meromorphic function with given zero and pole orders at the marked points. When trying to compactify this cycle over the whole moduli space of stable curves, it turns out that the compactification naturally lives inside an iterated boundary blow-up of the moduli space. This leads to the notion of logarithmic Chow groups, describing the intersection theory of all such blow-ups simultaneously. In the talk I will explain this story and describe how stability conditions on line bundles can be used to calculate a formula for the logarithmic compactification of the double-ramification locus. This is joint work with D. Holmes, S. Molcho, R. Pandharipande and A. Pixton.