John Lesieutre : Constraints on positive entropy automorphisms of smooth threefolds

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

At

March 18, 2015, 4 p.m.

In

SEO 427

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.