RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 4, Pages 100–128 (Mi izv8782)  

Birationally rigid complete intersections of high codimension

D. Evans, A. V. Pukhlikov

Department of Mathematical Sciences, University of Liverpool

Abstract: We prove that a Fano complete intersection of codimension $k$ and index 1 in the complex projective space ${\mathbb P}^{M+k}$ for $k\geqslant 20$ and $M\geqslant 8k\log k$ 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 $\frac12 (M-5k)(M-6k)$. The proof is based on the techniques of hypertangent divisors combined with the recently discovered $4n^2$-inequality for complete intersection singularities.

Keywords: birational rigidity, maximal singularity, multiplicity, hypertangent divisor, complete intersection singularity.

Funding Agency Grant Number
Leverhulme Trust RPG-2016-279


DOI: https://doi.org/10.4213/im8782

Full text: PDF file (757 kB)
First page: PDF file
References: PDF file   HTML file

English version:
DOI: https://doi.org/10.1070/IM8782

UDC: 512.76
MSC: 14E05, 14E07
Received: 07.03.2018

Citation: D. Evans, A. V. Pukhlikov, “Birationally rigid complete intersections of high codimension”, Izv. RAN. Ser. Mat., 83:4 (2019), 100–128

Citation in format AMSBIB
\Bibitem{EvaPuk19}
\by D.~Evans, A.~V.~Pukhlikov
\paper Birationally rigid complete intersections of high codimension
\jour Izv. RAN. Ser. Mat.
\yr 2019
\vol 83
\issue 4
\pages 100--128
\mathnet{http://mi.mathnet.ru/izv8782}
\crossref{https://doi.org/10.4213/im8782}
\elib{http://elibrary.ru/item.asp?id=38590298}


Linking options:
  • http://mi.mathnet.ru/eng/izv8782
  • https://doi.org/10.4213/im8782
  • http://mi.mathnet.ru/eng/izv/v83/i4/p100

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
    Number of views:
    This page:42
    References:7
    First page:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019