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



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2017, Volume 102, Issue 4, Pages 549–558 (Mi mz11208)  

Birationally Rigid Singular Double Quadrics and Double Cubics

E. Johnstone

University of Liverpool, United Kingdom

Abstract: 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.

DOI: https://doi.org/10.4213/mzm11208

Full text: PDF file (501 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2017, 102:4, 508–515

Bibliographic databases:

UDC: 512.7
Received: 10.04.2016
Revised: 17.11.2016

Citation: E. Johnstone, “Birationally Rigid Singular Double Quadrics and Double Cubics”, Mat. Zametki, 102:4 (2017), 549–558; Math. Notes, 102:4 (2017), 508–515

Citation in format AMSBIB
\Bibitem{Joh17}
\by E.~Johnstone
\paper Birationally Rigid Singular Double Quadrics and Double Cubics
\jour Mat. Zametki
\yr 2017
\vol 102
\issue 4
\pages 549--558
\mathnet{http://mi.mathnet.ru/mz11208}
\crossref{https://doi.org/10.4213/mzm11208}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3706871}
\elib{http://elibrary.ru/item.asp?id=30512290}
\transl
\jour Math. Notes
\yr 2017
\vol 102
\issue 4
\pages 508--515
\crossref{https://doi.org/10.1134/S000143461709022X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000413455100022}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85032004671}


Linking options:
  • http://mi.mathnet.ru/eng/mz11208
  • https://doi.org/10.4213/mzm11208
  • http://mi.mathnet.ru/eng/mz/v102/i4/p549

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:150
    References:18
    First page:12

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