## Geometry and Topology Seminar - David Stapleton - Hypersurfaces which are far from being rational

- Calendar
- Mathematics & Statistics

- Date
- 01.15.2020 3:30 pm - 4:30 pm

### Description

HH 217

David Stapleton

Title:Hypersurfaces which are farfrom being rational

Abstract: Rational varieties aresome of the simplest examples of varieties, e.g. most of their points can beparametrized by affine space. It is natural to ask (1) How can we determinewhen a variety is rational? and (2) If a variety is not rational, can wemeasure how far it is from being rational? A famous particular case of thisproblem is when the variety is a smooth hypersurface in projectivespace. This problem has attracted a great deal of attention bothclassically and recently. The interesting case is when the degree of thehypersurface is at most the dimension of the projective space (the ``Fano"range) as these hypersurfaces share many of the properties of projective space.In this talk, we present a recent result, joint with Nathan Chen, which saysthat smooth Fano hypersurfaces of large dimension can have arbitrarily largedegrees of irrationality, i.e. they can be arbitrarily far from being rational.

David Stapleton

Title:Hypersurfaces which are farfrom being rational

Abstract: Rational varieties aresome of the simplest examples of varieties, e.g. most of their points can beparametrized by affine space. It is natural to ask (1) How can we determinewhen a variety is rational? and (2) If a variety is not rational, can wemeasure how far it is from being rational? A famous particular case of thisproblem is when the variety is a smooth hypersurface in projectivespace. This problem has attracted a great deal of attention bothclassically and recently. The interesting case is when the degree of thehypersurface is at most the dimension of the projective space (the ``Fano"range) as these hypersurfaces share many of the properties of projective space.In this talk, we present a recent result, joint with Nathan Chen, which saysthat smooth Fano hypersurfaces of large dimension can have arbitrarily largedegrees of irrationality, i.e. they can be arbitrarily far from being rational.

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