Geodesic
Birationally Rigid Singular Double Quadrics and Double Cubics
Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 549-558

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper it is shown that Fano double quadrics of index 1 and dimension at least 6 are birationally superrigid if the branch divisor has at most quadratic singularities of rank at least 6. Fano double cubics of index 1 and dimension at least 8 are birationally superrigid if the branch divisor has at most quadratic singularities of rank at least 8 and another minor condition of general position is satisfied. Hence, in the parameter spaces of these varieties the complement to the set of factorial and birationally superrigid varieties is of codimension at least $\binom{M-4}{2}+1$ and $\binom{M-6}{2}+1$ respectively.
Keywords: algebraic geometry, birational geometry, birational rigidity, Fano variety. 
@article{MZM_2017_102_4_a6,
     author = {E. Johnstone},
     title = {Birationally {Rigid} {Singular} {Double} {Quadrics} and {Double} {Cubics}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {549--558},
     publisher = {mathdoc},
     volume = {102},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a6/}
}
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E. Johnstone. Birationally Rigid Singular Double Quadrics and Double Cubics. Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 549-558. http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a6/