Birationally rigid complete intersections of high codimension

Abstract

We prove that a Fano complete intersection of codimension $k$ and index 1 in the complex projective space ${\mathbb{P}}^{M+k}$ for $k⩾20$ and $M⩾8k\log k$ with at most multi-quadratic singularities is birationally superrigid. The codimension of the complement to the set of birationally superrigid complete intersections in the natural parameter space is shown to be at least $\frac{1}{2}(M-5k)(M-6k)$. The proof is based on the techniques of hypertangent divisors combined with the recently discovered $4n^2$-inequality for complete intersection singularities.

arXiv comment29 pages

References in corpus (9)

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Cited by in corpus (3)

• Birational superrigidity and K-stability of singular Fano complete intersections
• Birational superrigidity and K-stability of Fano complete intersections of index one (with an appendix written jointly with Charlie Stibitz)
• $2n^2$-inequality for $c{A}_1$ points and applications to birational rigidity