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Tr. Mat. Inst. Steklova, 2019, Volume 307, Pages 254–266 (Mi tm4026)  

Birationally Rigid Finite Covers of the Projective Space

A. V. Pukhlikov

Department of Mathematical Sciences, The University of Liverpool, Liverpool, L69 7ZL, UK

Abstract: In this paper we prove birational superrigidity of finite covers of degree $d$ of the $M$-dimensional projective space of index $1$, where $d\geq 5$ and $M\geq 10$, that have at most quadratic singularities of rank ${\geq } 7$ and satisfy certain regularity conditions. Up to now, only cyclic covers have been studied in this respect. The set of varieties that have worse singularities or do not satisfy the regularity conditions is of codimension ${\geq } (M-4)(M-5)/2+1$ in the natural parameter space of the family.

Funding Agency Grant Number
Leverhulme Trust RPG-2016-279
The work was supported by the Leverhulme Trust (Research Project Grant RPG-2016-279).


DOI: https://doi.org/10.4213/tm4026

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 307, 232–244

Bibliographic databases:

UDC: 512.763+512.765
Received: January 7, 2019
Revised: May 1, 2019
Accepted: August 26, 2019

Citation: A. V. Pukhlikov, “Birationally Rigid Finite Covers of the Projective Space”, Algebra, number theory, and algebraic geometry, Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich, Tr. Mat. Inst. Steklova, 307, Steklov Mathematical Institute of RAS, Moscow, 2019, 254–266; Proc. Steklov Inst. Math., 307 (2019), 232–244

Citation in format AMSBIB
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\paper Birationally Rigid Finite Covers of the Projective Space
\inbook Algebra, number theory, and algebraic geometry
\bookinfo Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich
\serial Tr. Mat. Inst. Steklova
\yr 2019
\vol 307
\pages 254--266
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
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\crossref{https://doi.org/10.4213/tm4026}
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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