David Stapleton : Irrationality of Fano hypersurfaces

Posted by Geoffrey Smith , part of the Algebraic Geometry Seminar.

At

Oct. 12, 2020, 4 p.m.

In

Zoom

Abstract

The degree of irrationality measures how far a variety is from being rational. In the case of curves the degree of irrationality coincides with the gonality, which is controlled by the positivity of the canonical bundle. In higher dimensions, the positivity of the canonical bundle plays an important role in controlling the degree of irrationality but it is interesting to ask what can be said when the canonical bundle is antiample. In this talk we discuss joint work with Nathan Chen where we show that Fano hypersurfaces can have arbitrarily large degrees of irrationality. We follow a degeneration to characteristic p argument of Kollár, where specializations of hypersurfaces can admit many holomorphic forms.