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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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Linking options:
http://mi.mathnet.ru/eng/izv2800https://doi.org/10.4213/im2800 http://mi.mathnet.ru/eng/izv/v74/i4/p119
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:
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V. A. Krasnov, “On real quadric line complexes”, Izv. Math., 74:6 (2010), 1255–1276
-
V. A. Krasnov, “Rigid Isotopy Classification of Real Quadric Line Complexes and Associated Kummer Surfaces”, Math. Notes, 89:5 (2011), 661–671
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V. A. Krasnov, “Real $GM$-Biquadrics”, Math. Notes, 89:6 (2011), 830–838
-
V. A. Krasnov, “On intersections of two real quadrics”, Izv. Math., 82:1 (2018), 91–139
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