Geodesic
Birationally Rigid Finite Covers of the Projective Space
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 254-266

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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.
Keywords: maximal singularity, linear system, Fano variety, self-intersection, hypertangent divisor.
Mots-clés : birational map 
@article{TM_2019_307_a13,
     author = {A. V. Pukhlikov},
     title = {Birationally {Rigid} {Finite} {Covers} of the {Projective} {Space}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {254--266},
     publisher = {mathdoc},
     volume = {307},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2019_307_a13/}
}
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A. V. Pukhlikov. Birationally Rigid Finite Covers of the Projective Space. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 254-266. http://geodesic.mathdoc.fr/item/TM_2019_307_a13/