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Localization-type theorems for families of curves

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If you have a question about this talk, please contact Dhruv Ranganathan .

Given a smooth projective variety X with an action of a torus T, the localization theorem describes the equivariant cohomology of X inside the equivariant cohomology of the fixed point locus of the action. In this talk, I will describe how this sort of structure persists for various geometrically meaningful subrings of the cohomology (or Chow) ring of any smooth S with a normal crossings divisor, even though no group action is present. I will then specialize to subrings that originate from a family of curves over S—for example, the tautological ring of the moduli space of curves, which originates from the universal family of the moduli space—and discuss how this formalism allows to calculate the classes of several loci in S, coming from Gromov-Witten theory and Brill-Noether theory.

This talk is part of the Algebraic Geometry Seminar series.

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