Abstract:
This paper is devoted to describing properties of complete
intersections of two real projective quadrics. For brevity we call
such varieties biquadrics. One of the main sections is devoted
to real projective spaces on real biquadrics. In another main section
we study the topology of the real parts of biquadrics. The other
sections are auxiliary.
Keywords:
quadric, biquadric, pencil of quadrics, index function, rigid isotopy classification,
topological type.
\Bibitem{Kra18}
\by V.~A.~Krasnov
\paper On intersections of two real quadrics
\jour Izv. Math.
\yr 2018
\vol 82
\issue 1
\pages 91--139
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https://www.mathnet.ru/eng/im8535
https://doi.org/10.1070/IM8535
https://www.mathnet.ru/eng/im/v82/i1/p97
This publication is cited in the following 5 articles:
Sarah Frei, Lena Ji, “A threefold violating a local-to-global principle for rationality”, Res. number theory, 10:2 (2024)
V. Oganesyan, “Zoo of monotone Lagrangians in ${\mathbb {C}}P^n$”, Sel. Math. New Ser., 29:5 (2023), 82
V. A. Krasnov, “The real Plücker–Klein map”, Izv. Math., 86:3 (2022), 456–507
B. Hassett, Yu. Tschinkel, J.-L. Colliot-Thelene, “Rationality of complete intersections of two quadrics over nonclosed fields”, Enseign. Math., 67:1-2 (2021), 1–44
A. Borisenko, Y. Nikolayevsky, “On cylindricity of submanifolds of nonnegative Ricci curvature in a Minkowski space”, J. Geom. Phys., 155 (2020), 103776
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