Birationally rigid complete intersections of high codimension

Evans, D and Pukhlikov, AV (2019) Birationally rigid complete intersections of high codimension. IZVESTIYA MATHEMATICS, 83 (4). pp. 743-769.

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Abstract

<jats:title>Abstract</jats:title> <jats:p> We prove that a Fano complete intersection of codimension <jats:inline-formula> <jats:tex-math><?CDATA $k$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="IZV_83_4_743ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> and index <jats:inline-formula> <jats:tex-math><?CDATA $1$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="IZV_83_4_743ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> in the complex projective space <jats:inline-formula> <jats:tex-math><?CDATA ${\mathbb P}^{M+k}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="IZV_83_4_743ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> for <jats:inline-formula> <jats:tex-math><?CDATA $k\ge 20$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="IZV_83_4_743ieqn4.gif" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $M\ge 8k\log k$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="IZV_83_4_743ieqn5.gif" xlink:type="simple" /> </jats:inline-formula> with at most multi-quadratic singularities is birationally superrigid. The codimension of the complement of the set of birationally superrigid complete intersections in the natural moduli space is shown to be at least <jats:inline-formula> <jats:tex-math><?CDATA $(M-5k)(M-6k)/2$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="IZV_83_4_743ieqn6.gif" xlink:type="simple" /> </jats:inline-formula>. The proof is based on the technique of hypertangent divisors combined with the recently discovered <jats:inline-formula> <jats:tex-math><?CDATA $4n^2$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="IZV_83_4_743ieqn7.gif" xlink:type="simple" /> </jats:inline-formula>-inequality for complete intersection singularities. </jats:p>

Item Type:	Article
Uncontrolled Keywords:	birational rigidity, maximal singularity, multiplicity, hypertangent divisor, complete intersection singularity
Depositing User:	Symplectic Admin
Date Deposited:	17 Oct 2018 10:51
Last Modified:	26 Jun 2023 14:49
DOI:	10.1070/IM8782
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3027532