Back to Algebraic Geometry Seminar: Fall 2024
Algebraic Geometry Seminar
Date: Tuesday, Dec 3, 2024
Time: 3:30PM - 4:30PM
Location: LCB 222
Morena Porzio
Columbia University
Title |
On the stable birationality of Hilbert schemes of points on surfaces |
Abstract |
In this talk, we will address the question for which pairs of integers (n,n’) the variety Hilb^n_X is stably birational to Hilb^n’_X, when X is a surface with H^1(X,O_X)=0. In order to do so we will relate the existence of degree n’ effective cycles on X with the existence of degree n ones using curves on X. We will then focus on geometrically rational surfaces, proving that there are only finitely many stable birational classes among the Hilb^n_X ’s. If time permits, we will prove the rationality of a generalization of the Hasse-Weil zeta function Z(X, t) in K_0(Var/k)/([A^1_k])[[t]] when char(k) = 0 and X is geometrically rational. |
Algebraic Geometry