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 ≥ 5 and M ≥ 10, that have at most quadratic singularities of rank ≥ 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 ≥ (M − 4)(M − 5)/2 + 1 in the natural parameter space of the family.
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Acknowledgments
The author is grateful to the colleagues in the Departments of Algebraic Geometry and Algebra of the Steklov Mathematical Institute for their interest in his work, as well as to the colleagues in algebraic geometry at the University of Liverpool for general support.
Funding
The work was supported by the Leverhulme Trust (Research Project Grant RPG-2016-279).
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This article was submitted by the author simultaneously in Russian and English
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Vol. 307, pp. 254–266.
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Pukhlikov, A.V. Birationally Rigid Finite Covers of the Projective Space. Proc. Steklov Inst. Math. 307, 232–244 (2019). https://doi.org/10.1134/S0081543819060142
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DOI: https://doi.org/10.1134/S0081543819060142