Geodesic
Real Two-Dimensional Intersections of a Quadric by a Cubic
Matematičeskie zametki, Tome 90 (2011) no. 4, pp. 530-540.

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The paper is devoted to finding the rigid isotopy classes of real projective surfaces that are obtained from nonsingular cubic sections of a chosen nonsingular real quadric. The result thus obtained is used to find the topological type of the real part of the Fano variety for the last rough projective class of real four-dimensional cubics which remained not investigated.
Keywords: real projective surface, rigid isotopy class, nonsingular cubic section, real four-dimensional cubic, homology group, Euler characteristic. 
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V. A. Krasnov. Real Two-Dimensional Intersections of a Quadric by a Cubic. Matematičeskie zametki, Tome 90 (2011) no. 4, pp. 530-540. http://geodesic.mathdoc.fr/item/MZM_2011_90_4_a4/

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

[2] B. Saint-Donat, “Projective models of $K-3$ surfaces”, Amer. J. Math., 96:4 (1974), 602–639 | DOI | MR | Zbl

[3] V. V. Nikulin, “Tselochislennye simmetricheskie bilineinye formy i nekotorye ikh geometricheskie prilozheniya”, Izv. AN SSSR. Ser. matem., 43:1 (1979), 111–177 | MR | Zbl

[4] V. V. Nikulin, “O komponentakh svyaznosti modulei veschestvennykh polyarizovannykh $\mathrm K3$-poverkhnostei”, Izv. RAN. Ser. matem., 72:1 (2008), 99–122 | MR | Zbl

[5] S. Finashin, V. Kharlamov, “Deformation classes of real four-dimensional cubic hypersurfaces”, J. Algebraic Geom., 17:4 (2008), 677–707 | MR | Zbl

[6] V. A. Krasnov, “Ekvivariantnaya topologicheskaya klassifikatsiya mnogoobrazii Fano veschestvennykh chetyrekhmernykh kubik”, Matem. zametki, 85:4 (2009), 603–615 | MR | Zbl

[7] V. A. Krasnov, “O mnogoobrazii Fano odnogo klassa veschestvennykh chetyrekhmernykh kubik”, Matem. zametki, 85:5 (2009), 711–720 | MR | Zbl

[8] S. Finashin, V. Kharlamov, “Topology of real cubic foufolds”, J. Topol., 3:1 (2010), 1–28, arXiv: math.AG/0906.1480v1 | MR | Zbl

[9] C. H. Clemens, P. A. Griffiths, “The intermediate Jacobian of the cubic threefold”, Ann. of Math. (2), 95:2 (1972), 281–356 | DOI | MR | Zbl