Presented By: Algebraic Geometry Seminar - Department of Mathematics
Algebraic Geometry Seminar: On the stable birationality of Hilbert schemes of points on surfaces
Morena Porzio (Columbia University)
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. As a corollary, we deduce 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.
We will then focus on geometrically rational surfaces, proving that there are only finitely many stable birational classes among the Hilb^n_X 's. As a corollary, we deduce 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.
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