Geodesic
Equivariant Topological Classification of the Fano Varieties of Real Four-Dimensional Cubics
Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 603-615.

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The equivariant topological type of the Fano variety parametrizing the set of lines on a nonsingular real hypersurface of degree three in a five-dimensional projective space is calculated. In the investigation of this Fano variety, results and constructions of the paper by Finashin and Kharlamov on the rigid projective classification of real four-dimensional cubics are used. The construction of Hassett (from the paper devoted to special four-dimensional cubics) is also applied.
Keywords: threefold, Fano variety, equivariant topological type, complex projective space, cubic fourfold, Grassman manifold, equivariant diffeomorphism, K3 surface. 
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V. A. Krasnov. Equivariant Topological Classification of the Fano Varieties of Real Four-Dimensional Cubics. Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 603-615. http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a9/

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

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

[3] A. B. Altman, S. L. Kleiman, “Foundations of the theory of Fano schemes”, Compositio Math., 34:1 (1977), 3–47 | MR | Zbl

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

[5] S. Finashin, V. Kharlamov, “Deformation classes of real four-dimensional cubic hypersurfaces”, J. Algebraic Geom., 17:4 (2008), 677–707 ; arXiv: math.AG/0607137 | MR | Zbl

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

[7] B. Hassett, “Special cubic fourfolds”, Compositio Math., 120:1 (2000), 1–23 | DOI | MR | Zbl

[8] Dzh. Milnor, Osobye tochki kompleksnykh giperpoverkhnostei, Mir, M., 1971 | MR | Zbl

[9] V. I. Arnold, A. N. Varchenko, S. M. Gusein-Zade, Osobennosti differentsiruemykh otobrazhenii. Monodromiya i asimptotika integralov, Nauka, M., 1984 | MR | Zbl

[10] B. G. Moishezon, “Ob $n$-mernykh kompaktnykh kompleksnykh mnogoobraziyakh, imeyuschikh $n$ algebraicheski nezavisimykh meromorfnykh funktsii. I”, Izv. AN SSSR. Ser. matem., 30:1 (1966), 133–174 | MR | Zbl

[11] J. Kollár, “The structure of algebraic threefolds: an introduction to Mori's program”, Bull. Amer. Math. Soc. (N.S.), 17:2 (1987), 211–273 | DOI | MR | Zbl

[12] V. A. Krasnov, “Deformatsii kompleksno-analiticheskikh modifikatsii”, Izv. AN SSSR. Ser. matem., 37:3 (1973), 516–532 | MR | Zbl

[13] A. Beauville, R. Donagi, “La variété des droites d'une hypersurface cubique de dimension 4”, C. R. Acad. Sci. Paris Sér. I Math., 301:14 (1985), 703–706 | MR | Zbl

[14] V. A. Krasnov, “Zhestkaya izotopicheskaya klassifikatsiya veschestvennykh trekhmernykh kubik”, Izv. RAN. Ser. matem., 70:4 (2006), 91–134 | MR | Zbl