Mihai Fulger : Kernels of numerical pushforwards

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

At

Sept. 24, 2014, 4 p.m.

In

SEO 427

Abstract

If $\pi:X\to Y$ is a morphism of projective varieties over an algebraically closed field, and $Z$ is an effective $k$-cycle on $X$, then $\pi_*Z=0$ iff $Z$ is a combination of subvarieties of $X$ that are contracted by $\pi$. When working not with cycles, but with cycle classes (modulo numerical equivalence), it is natural to ask when can we expect a similar geometric conclusion given the vanishing of a class $\pi_*\alpha$. I will present progress on this question, in particular leading to new cases of two conjectures essentially due to Debarre, Jiang, and Voisin. This is joint work with B. Lehmann.