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Mathematics > Algebraic Geometry

arXiv:1812.10980 (math)
[Submitted on 28 Dec 2018]

Title:Effective birational rigidity of Fano double hypersurfaces

Authors:Thomas Eckl, Aleksandr Pukhlikov
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Abstract:We prove birational superrigidity of Fano double hypersurfaces of index one with quadratic and multi-quadratic singularities, satisfying certain regularity conditions, and give an effective explicit lower bound for the codimension of the set of non-rigid varieties in the natural parameter space of the family. The lower bound is quadratic in the dimension of the variety. The proof is based on the techniques of hypertangent divisors combined with the recently discovered $4n^2$-inequality for complete intersection singularities.
Comments: 16 pages
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14E05, 14E07
Cite as: arXiv:1812.10980 [math.AG]
  (or arXiv:1812.10980v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.10980

Submission history

From: Aleksandr Pukhlikov [view email]
[v1] Fri, 28 Dec 2018 12:56:56 UTC (13 KB)
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