Harvard-MIT Algebraic Geometry Seminar

Tuesday, October 12, 2021 at 3:00pm to 4:00pm

Harvard Science Center, SC-507 1 Oxford St, Cambridge, MA 02138

Featured Speaker: Hannah Larson (Stanford)

Title: Chow rings of low-degree Hurwitz spaces.

The Chow ring of a variety packages information about its subvarieties and how they intersect (a sort of "algebraic version" of the cohomology ring). When studying Chow rings of moduli spaces, there are often certain "tautological" classes that arise naturally from the moduli problem. While determining the full Chow ring of a moduli space may be difficult, the subring generated by tautological classes may have a nicer structure. This motivates two questions: (1) What is the structure of the tautological ring? (2) To what extent are all classes tautological? I'll start by giving some background about these questions for the moduli space of curves M_g, and explain how they also motivated us to study Hurwitz spaces H_{k,g}, parametrizing degree k, genus g covers of P^1. Then, I'll give some results addressing (1) and (2) for the Hurwitz spaces H_{k,g} for k \leq 5. This is joint work with Samir Canning.

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