Jason Starr : Spaces of Rational Curves on Fano Manifolds

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

Feb. 24, 2016, 4 p.m.

In

SEO 427

Abstract

A projective manifold is "Fano" if the expected dimension of the parameter space of rational curves of a given effective curve class increases with the multiple of that class. A conjecture of Cohen-Jones-Segal predicts the topology of these parameter spaces. I will focus on the simplest Fano manifolds, general low degree hypersurfaces in projective space. I will explain work of Riedl-Yang on irreducibility of the parameter spaces, joint work with Zhiyu Tian on the Picard groups, and joint work with Coskun and Harris that gives the nef cones.