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Birationally rigid Fano threefold hypersurfaces

About this Title

Ivan Cheltsov, School of Mathematics, The University of Edinburgh, Edinburgh, EH9 3JZ, United Kingdom and Jihun Park, Center for Geometry and Physics, Institute for Basic Science (IBS) 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk, 790-784, Korea – and – Department of Mathematics, POSTECH 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk, 790-784, Korea

Publication: Memoirs of the American Mathematical Society
Publication Year: 2017; Volume 246, Number 1167
ISBNs: 978-1-4704-2316-2 (print); 978-1-4704-3643-8 (online)
Published electronically: December 6, 2016
Keywords: Fano hypersurface, weighted projective space, birationally rigid; birational involution
MSC: Primary 14E07, 14E08, 14J30, 14J45, 14J70

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Table of Contents


  • 1. Introduction
  • 2. Smooth points and curves
  • 3. Singular points
  • 4. Birational involutions
  • 5. Proof of Main Theorem
  • 6. Epilogue


We prove that every quasi-smooth weighted Fano threefold hypersurface in the 95 families of Fletcher and Reid is birationally rigid.

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