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Intersection theory on low-degree Hurwitz spaces 

Hannah Larson (Stanford)
Tuesday, December 8, 2020 - 2:30pm
via Zoom
Hannah Larson

While there is much work and conjectures surrounding the intersection theory of the moduli space of curves, relatively little is known about the intersection theory of the Hurwitz space H_{k, g} parametrizing smooth degree k, genus g covers of P^1. For k = 3, 4, 5, I will present a stabilization result for the rational Chow rings of H_{k,g} as g tends to infinity. In the case k = 3, we completely determine the Chow ring. As a corollary, we prove that the Chow groups of the simply branched Hurwitz space are zero in codimension up to roughly g/k for k = 3, 4, 5. This is joint work with Sam Canning.

The talk will start with a pre-seminar at 2pm:

Title: Chow rings and associated scrolls
Abstract: I will define Chow rings and their basic properties needed for the talk. I will also discuss the associated scroll construction for a degree k cover of P^1 and a generalization for any Gorenstein degree k cover.


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