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The degree of irrationality of hypersurfaces in various Fano varieties

  • David StapletonEmail author
  • Brooke Ullery
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  • 15 Downloads

Abstract

The purpose of this paper is to compute the degree of irrationality of hypersurfaces of sufficiently high degree in various Fano varieties: quadrics, Grassmannians, products of projective space, cubic threefolds, cubic fourfolds, and complete intersection threefolds of type (2,2). This extends the techniques of Bastianelli, De Poi, Ein, Lazarsfeld, and the second author who computed the degree of irrationality of hypersurfaces of sufficiently high degree in projective space. A theme in the paper is that the fibers of low degree rational maps from the hypersurfaces to projective space tend to lie on curves of low degree contained in the Fano varieties. This allows us to study these maps by studying the geometry of curves in these Fano varieties.

Mathematics Subject Classification

14E05 14N20 

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of California San DiegoSan DiegoUSA

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