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Hilbert Schemes and Newton-Okounkov Bodies

Ian Casey
March 1, 2022
3:00 pm - 4:00 pm
MW 154

Title:  Hilbert Schemes and Newton-Okounkov Bodies

Speaker:  Ian Cavey (Ohio State)

Speaker's URL:  https://math.osu.edu/people/cavey.14

Abstract:  The Hilbert scheme of $n$ points in the plane parametrizes finite, length $n$ subschemes of $\mathbb{C}^2$. In this talk I will explain how to compute the Newton-Okounkov body of this Hilbert scheme. Newton-Okounkov bodies are convex sets that encode geometric information about the underlying space. In this case, the Newton-Okounkov body turns out to be an (unbounded) polyhedron which we can describe explicitly. If time permits, I will also discuss partial results for the Hilbert schemes of points on toric surfaces.

URL associated with Seminar
https://research.math.osu.edu/agseminar/

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Seminar - Algebraic Geometry