Geodesic
Fano Surfaces of Real Quartics
Matematičeskie zametki, Tome 81 (2007) no. 1, pp. 83-97.

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We prove certain properties of the Fano surface of bitangents to the real quartic in projective 3-space. In particular, we estimate the dimension of the cohomology of the real part of this surface in terms of the dimension of the cohomology of the real part of the quartic, and compute its Euler characteristic.
Keywords: real algebraic varieties, Fano surface, Euler characteristic.
Mots-clés : quartic 
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V. A. Krasnov. Fano Surfaces of Real Quartics. Matematičeskie zametki, Tome 81 (2007) no. 1, pp. 83-97. http://geodesic.mathdoc.fr/item/MZM_2007_81_1_a6/

[1] G. E. Welters, Abel–Jacobi Isogenies for Certain Types of Fano Threefolds, Math. Centre Tracts, 141, North-Holland, Amsterdam, 1981 | MR | Zbl

[2] H. G. Zeuthen, “Sur les différentes formes des courbes planes du quatrième ordre”, Math. Ann., 7 (1874), 410–432 | Zbl

[3] V. M. Kharlamov, “Topologicheskie tipy neosobykh poverkhnostei stepeni 4 v $\mathbb{RP}^3$”, Funktsion. analiz i ego prilozh., 10:4 (1976), 55–68 | MR | Zbl

[4] V. M. Kharlamov, “Izotopicheskie tipy neosobykh poverkhnostei stepeni 4 v $\mathbb{RP}^3$”, Funktsion. analiz i ego prilozh., 12:1 (1978), 86–87 | MR | Zbl

[5] C. H. Clemens, “Double solids”, Adv. Math., 47:2 (1983), 107–230 | DOI | MR | Zbl

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

[7] G. Bredon, Vvedenie v teoriyu kompaktnykh grupp preobrazovanii, Nauka, M., 1980 | MR | Zbl

[8] V. A. Krasnov, “Ob ekvivariantnykh kogomologiyakh Grotendika veschestvennogo algebraicheskogo mnogoobraziya i ikh prilozheniyakh”, Izv. RAN. Ser. matem., 58:3 (1994), 36–52 | MR | Zbl

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

[10] A. Grotendik, O nekotorykh voprosakh gomologicheskoi algebry, IL, M., 1961 | Zbl

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

[12] A. N. Tyurin, “Pyat lektsii o trekhmernykh mnogoobraziyakh”, UMN, 27:5 (1972), 3–50 | MR | Zbl