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Birationally Rigid Complete Intersections with a Singular Point of High Multiplicity

Part of: Birational geometry

Published online by Cambridge University Press:  26 September 2018

A. V. Pukhlikov
A. V. Pukhlikov*
Affiliation:
Department of Mathematical Sciences, Peach Street, The University of Liverpool, Liverpool L69 7ZL, UK (pukh@liverpool.ac.uk)
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Abstract

We prove the birational rigidity of Fano complete intersections of index 1 with a singular point of high multiplicity, which can be close to the degree of the variety. In particular, the groups of birational and biregular automorphisms of these varieties are equal, and they are non-rational. The proof is based on the techniques of the method of maximal singularities, the generalized 4n2-inequality for complete intersection singularities and the technique of hypertangent divisors.

Keywords

birational rigiditymaximal singularitymultiplicityhypertangent divisorcomplete intersection singularity

MSC classification

Primary: 14E05: Rational and birational maps
Secondary: 14E07: Birational automorphisms, Cremona group and generalizations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 1 , February 2019 , pp. 221 - 239
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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Footnotes

Dedicated to Yu. I. Manin on the occasion of his 80th birthday

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