Ian Cavey : Hilbert Schemes and Newton-Okounkov Bodies

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

April 18, 2022, 3 p.m.

In

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Abstract

The Hilbert scheme of n points in the (affine) plane parametrizes finite, length n subschemes of C^2. In this talk I will explain how to compute the “Newton-Okounkov bodies” of these Hilbert schemes. These Newton-Okounkov bodies are (unbounded) polyhedra which encode geometric information about the Hilbert schemes. I will also discuss some partial results and conjectures for Hilbert schemes of points on complete toric surfaces.