Geodesic
Real $GM$-Biquadrics
Matematičeskie zametki, Tome 89 (2011) no. 6, pp. 868-878.

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We consider real algebraic varieties that are the intersection of two real quadrics. For brevity, we refer to such varieties as real biquadrics. The rigid isotopy classes of real biquadrics have been described long ago. In the present paper, we find the rigid isotopy classes in which the biquadrics are $GM$-varieties.
Keywords: rigid isotopy class, real biquadric, $GM$-variety, cohomology group, complex projective algebraic variety, Grassmann variety, spectral sequence. 
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     author = {V. A. Krasnov},
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V. A. Krasnov. Real $GM$-Biquadrics. Matematičeskie zametki, Tome 89 (2011) no. 6, pp. 868-878. http://geodesic.mathdoc.fr/item/MZM_2011_89_6_a6/

[1] V. A. Rokhlin, “Kompleksnye topologicheskie kharakteristiki veschestvennykh algebraicheskikh krivykh”, UMN, 33:5 (1978), 77–89 | MR | Zbl

[2] A. Degtyarev, I. Itenberg, V. Kharlamov, Real Enriques Surfaces, Lecture Notes in Math., 1746, Springer-Verlag, Berlin, 2000 | DOI | MR | Zbl

[3] V. A. Krasnov, “Neravenstva Garnaka–Toma dlya otobrazhenii veschestvennykh algebraicheskikh mnogoobrazii”, Izv. AN SSSR. Ser. matem., 47:2 (1983), 268–297 | MR | Zbl

[4] V. A. Krasnov, “Veschestvennye trekhmernye bikvadriki”, Izv. RAN. Ser. matem., 74:4 (2010), 119–144

[5] A. A. Agrachev, R. V. Gamkrelidze, “Kvadratichnye otobrazheniya i gladkie vektor- funktsii: eilerovy kharakteristiki mnozhestv urovnya”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Nov. dostizh., 35, VINITI, M., 1989, 179–239 | MR | Zbl

[6] A. A. Agrachev, “Gomologii peresechenii veschestvennykh kvadrik”, Dokl. AN SSSR, 299:5 (1988), 1033–1036 | MR | Zbl

[7] A. Degtyarev, I. Itenberg, V. Kharlamov, On the Number of Components of a Complete Intersection of Real Quadrics, arXiv: math.AG/0806.4077

[8] V. A. Krasnov, “Veschestvennye algebraicheskie GM-mnogoobraziya”, Izv. RAN. Ser. matem., 62:3 (1998), 39–66 | MR | Zbl

[9] M. Reid, The Complete Intersection of Two or More Quadrics, Ph.D. Thesis, Cambridge, 1972