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Tr. Mat. Inst. Steklova, Forthcoming paper (Mi tm4026)  

Birationally rigid finite covers of the projective space

A. V. Pukhlikov

University of Liverpool

Abstract: In this paper we prove birational superrigidity of finite covers of degree $d$ of the $M$-dimensional projective space of index 1, where $d\geqslant 5$ and $M\geqslant 10$, with at most quadratic singularities of rank $\geqslant 7$, satisfying certain regularity conditions. Up to now, only cyclic covers were studied in this respect. The set of varieties with worse singularities or not satisfying the regularity conditions is of codimension $\geqslant\frac12(M-4)(M-5)+1$ in the natural parameter space of the family.

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

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

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  • http://mi.mathnet.ru/eng/tm4026
  • 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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