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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 4, Pages 119–144 (Mi izv2800)  

This article is cited in 4 scientific papers (total in 4 papers)

Real three-dimensional biquadrics

V. A. Krasnov

P. G. Demidov Yaroslavl State University

Abstract: We find the topological types of biquadrics (complete intersections of two real four-dimensional quadrics). The rigid isotopy classes of real three-dimensional biquadrics were described long ago: there are nine such classes. We find the correspondence between the topological types of real biquadrics and their rigid isotopy classes, and show that only two rigid isotopy classes have the same topological type. One of these classes consists of real $\operatorname{GM}$-varieties and the other contains no $\operatorname{GM}$-varieties. We also study the sets of real lines on real biquadrics.

Keywords: biquadric, discriminant hypersurface, maximal variety, intermediate Jacobian, Abelian surface.

DOI: https://doi.org/10.4213/im2800

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English version:
Izvestiya: Mathematics, 2010, 74:4, 781–804

Bibliographic databases:

UDC: 512.7
MSC: 14P25
Received: 14.05.2008

Citation: V. A. Krasnov, “Real three-dimensional biquadrics”, Izv. RAN. Ser. Mat., 74:4 (2010), 119–144; Izv. Math., 74:4 (2010), 781–804

Citation in format AMSBIB
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  • https://doi.org/10.4213/im2800
  • http://mi.mathnet.ru/eng/izv/v74/i4/p119

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    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. V. A. Krasnov, “On real quadric line complexes”, Izv. Math., 74:6 (2010), 1255–1276  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. A. Krasnov, “Rigid Isotopy Classification of Real Quadric Line Complexes and Associated Kummer Surfaces”, Math. Notes, 89:5 (2011), 661–671  mathnet  crossref  crossref  mathscinet  isi
    3. V. A. Krasnov, “Real $GM$-Biquadrics”, Math. Notes, 89:6 (2011), 830–838  mathnet  crossref  crossref  mathscinet  isi
    4. V. A. Krasnov, “On intersections of two real quadrics”, Izv. Math., 82:1 (2018), 91–139  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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