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Geometry & Topology SeminarExport this event to calendar

Friday, January 31, 2020 — 2:35 PM EST

Andrew Staal, Department of Pure Mathematics, University of Waterloo

"Ubiquity of Smooth Hilbert Schemes"

What are the geometric properties of a typical Hilbert scheme? In this talk, we consider Hilbert schemes parametrizing closed subschemes in some projective space with a fixed Hilbert polynomial. We first explain how the collection of all such Hilbert schemes forms a collection of trees and a discrete probability space.  Exploiting the underlying combinatorial structure, we show why a random Hilbert scheme is smooth and irreducible with probability greater than 0.5 and how to classify Hilbert schemes with unique Borel-fixed points.

MC 5403

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