Birationally Rigid Finite Covers of the Projective Space

Pukhlikov, AV (2019) Birationally Rigid Finite Covers of the Projective Space. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 307 (1). pp. 232-244.

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Official URL: http://dx.doi.org/10.1134/s0081543819060142

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.

Item Type:	Article
Additional Information:	16 pages
Uncontrolled Keywords:	math.AG, math.AG, 14E05, 14E07
Depositing User:	Symplectic Admin
Date Deposited:	12 Sep 2019 15:21
Last Modified:	19 Jan 2023 00:26
DOI:	10.1134/S0081543819060142
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3054387