# The nef cone of the Hilbert scheme of points on rational elliptic surfaces and the cone conjecture

## Algebra and Number Theory Seminar

## Meeting Details

For more information about this meeting, contact Allyson Borger, Kirsten Eisentraeger, Jack Huizenga, Mihran Papikian, Ae Ja Yee, John Lesieutre.

**Speaker:** John Kopper, PSU

**Abstract:** Hilbert schemes of points are classical spaces that parameterize collections of points on a fixed variety. In this talk I will explain how Hilbert schemes of points on rational elliptic surfaces give high-dimensional examples of "maximally complicated" varieties allowed by the Morrison-Kawamata cone conjecture, a conjecture that bounds how complicated the geometry of curves can be on certain algebraic varieties. More precisely, I will show that the nef cones of such Hilbert schemes are not finitely generated, but do have a fundamental domain for the action of the automorphism group.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 09/05/2019

**Time:** 11:00am - 11:50am