Algebraic Geometry Seminar
John Lesieutre
Institute for Advanced Study
Constraints on positive entropy automorphisms of smooth threefolds
Abstract: There are currently few known examples of automorphisms of smooth threefolds with positive entropy, i.e. for which the induced map on $N^1(X)$ has an eigenvalue larger than 1. I'll say a bit about why one might care, and what the situation is in dimension 2. Then I'll describe some constraints on smooth threefolds $X$ admitting such automorphisms. For example, I'll show that if $X$ is constructed as a blow-up of $\mathbb{P}^1 x \mathbb{P}^2$ or $\mathbb{P}^3$, any positive entropy automorphism admits an equivariant map to a surface. I'll also give a related example of a non-uniruled, terminal threefold with infinitely many $K_X$-negative extremal rays on the cone of curves.
Wednesday March 18, 2015 at 4:00 PM in SEO 427