Algebraic Geometry Seminar
Mihai Fulger
Princeton
Kernels of numerical pushforwards
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.
Wednesday September 24, 2014 at 4:00 PM in SEO 427