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. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2003, Volume 194, Number 11, Pages 95–116 (Mi msb782)  

This article is cited in 20 scientific papers (total in 20 papers)

Non-rationality of the 4-dimensional smooth complete intersection of a quadric and a quartic not containing planes

I. A. Cheltsov


Abstract: The non-rationality and the birational superrigidity is proved for the 4-dimensional smooth complete intersection of a quadric and a quartic in ${\mathbb P}^6$ that contains no 2-dimensional linear subspace of ${\mathbb P}^6$. It is also proved that such an intersection is not birationally isomorphic to an elliptic fibration.

DOI: https://doi.org/10.4213/sm782

Full text: PDF file (367 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2003, 194:11, 1679–1699

Bibliographic databases:

UDC: 513.6
MSC: Primary 14E05, 14E07, 14E08, 14E30, 14M20; Secondary 14C17, 14B05
Received: 21.03.2003

Citation: I. A. Cheltsov, “Non-rationality of the 4-dimensional smooth complete intersection of a quadric and a quartic not containing planes”, Mat. Sb., 194:11 (2003), 95–116; Sb. Math., 194:11 (2003), 1679–1699

Citation in format AMSBIB
\Bibitem{Che03}
\by I.~A.~Cheltsov
\paper Non-rationality of the~ 4-dimensional smooth complete intersection of
a~quadric and a~quartic not containing planes
\jour Mat. Sb.
\yr 2003
\vol 194
\issue 11
\pages 95--116
\mathnet{http://mi.mathnet.ru/msb782}
\crossref{https://doi.org/10.4213/sm782}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2041468}
\zmath{https://zbmath.org/?q=an:1071.14017}
\transl
\jour Sb. Math.
\yr 2003
\vol 194
\issue 11
\pages 1679--1699
\crossref{https://doi.org/10.1070/SM2003v194n11ABEH000782}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000220189500005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-1642292999}


Linking options:
  • http://mi.mathnet.ru/eng/msb782
  • https://doi.org/10.4213/sm782
  • http://mi.mathnet.ru/eng/msb/v194/i11/p95

    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

    This publication is cited in the following articles:
    1. I. A. Cheltsov, L. Votslav, “Nonrational Complete Intersections”, Proc. Steklov Inst. Math., 246 (2004), 303–307  mathnet  mathscinet  zmath
    2. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Cheltsov I., “On factoriality of nodal threefolds”, J. Algebraic Geom., 14:4 (2005), 663–690  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    4. Cheltsov I., “Birationally rigid del Pezzo fibrations”, Manuscripta Math., 116:4 (2005), 385–396  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    5. I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Pukhlikov A.V., “Birational geometry of algebraic varieties with a pencil of Fano complete intersections”, Manuscripta Math., 121:4 (2006), 491–526  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    7. I. A. Cheltsov, “Local inequalities and birational superrigidity of Fano varieties”, Izv. Math., 70:3 (2006), 605–639  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. Cheltsov I., “Double cubics and double quartics”, Math. Z., 253:1 (2006), 75–86  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    9. A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Cheltsov I., “On nodal sextic fivefold”, Math. Nachr., 280:12 (2007), 1344–1353  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    11. A. V. Pukhlikov, “On the self-intersection of a movable linear system”, J. Math. Sci., 164:1 (2010), 119–130  mathnet  crossref  mathscinet  elib
    12. Pukhlikov A.V., “Birational geometry of algebraic varieties with a pencil of Fano cyclic covers”, Pure Appl. Math. Q., 5:2, Special Issue: In honor of Friedrich Hirzebruch, Part 1 (2009), 641–700  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    13. A. V. Pukhlikov, “Birational geometry of Fano double spaces of index two”, Izv. Math., 74:5 (2010), 925–991  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. A. V. Pukhlikov, “Birationally rigid varieties. II. Fano fibre spaces”, Russian Math. Surveys, 65:6 (2010), 1083–1171  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. A. V. Pukhlikov, “Birationally rigid complete intersections of quadrics and cubics”, Izv. Math., 77:4 (2013), 795–845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. Odaka Yu., Okada T., “Birational Superrigidity and Slope Stability of Fano Manifolds”, Math. Z., 275:3-4 (2013), 1109–1119  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    17. A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150  mathnet  crossref  crossref  isi  elib
    18. Suzuki F., “Birational rigidity of complete intersections”, Math. Z., 285:1-2 (2017), 479–492  crossref  mathscinet  zmath  isi  scopus
    19. Evans D., Pukhlikov A., “Birationally Rigid Complete Intersections of Codimension Two”, Bull. Korean. Math. Soc., 54:5 (2017), 1627–1654  crossref  mathscinet  isi  scopus
    20. D. Evans, A. V. Pukhlikov, “Birationally rigid complete intersections of high codimension”, Izv. Math., 83:4 (2019), 743–769  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:245
    Full text:103
    References:38
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020