Geoffrey Smith : Very free rational curves in Fano varieties

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

At

Sept. 13, 2021, 3 p.m.

In

Zoom

Abstract

I will present a result allowing us to control the normal bundle of a rational curve in certain complete intersections in a variety X. In particular, given a rational curve C in X, under certain hypotheses this control allows us to find complete intersections in X such that the normal bundle to C in Y is "as general as possible." By using this tool, I will present some new examples of separably rational connected Fano varieties in arbitrary characteristic. For instance, a general Fano complete intersection of hypersurfaces of degree at least 3 in a Grassmannian is separably rationally connected in any characteristic. This talk is based on joint work with Izzet Coskun.