Talk page
Title:
Logarithmic double ramification cycles
Speaker:
Abstract:
Inside the moduli space of smooth genus g curves (C, p1, ..., pn) there is a natural locus, cut out by the condition that there exists a rational function on C with zeros and poles at the marked points pi of specified orders. The double ramification cycle DR is an algebraic cycle class extending the fundamental class of this locus to the moduli space Mbar of stable curves. However, from its construction one can see that DR naturally lives as a cycle on a blowup of Mbar. Hence it gives a class in the logarithmic Chow ring of Mbar, which describes the intersection theory of all (suitable) blowups of Mbar simultaneously. I will describe a recent result joint with Molcho, Holmes, Pandharipande and Pixton where we compute an explicit formula for this so-called logarithmic double ramification cycle. On the way, we will see how to describe classes in the logarithmic Chow ring using piecewise polynomials on the moduli space of tropical curves.
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