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Effective Birational Rigidity of Fano Double Hypersurfaces

Authors
  • Eckl, Thomas1
  • Pukhlikov, Aleksandr1
  • 1 The University of Liverpool, Department of Mathematical Sciences, Mathematical Sciences Building, Liverpool, England, L69 7ZL, UK , Liverpool (United Kingdom)
Type
Published Article
Journal
Arnold Mathematical Journal
Publisher
Springer International Publishing
Publication Date
Dec 01, 2018
Volume
4
Issue
3-4
Pages
505–521
Identifiers
DOI: 10.1007/s40598-019-00106-x
Source
Springer Nature
Keywords
License
Green

Abstract

We prove birational superrigidity of Fano double hypersurfaces of index one with quadratic and multi-quadratic singularities, satisfying certain regularity conditions, and give an effective explicit lower bound for the codimension of the set of non-rigid varieties in the natural parameter space of the family. The lower bound is quadratic in the dimension of the variety. The proof is based on the techniques of hypertangent divisors combined with the recently discovered 4n2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4n^2$$\end{document}-inequality for complete intersection singularities.

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