Geodesic
On the Fano Surface of a Real Cubic $M$-Threefold
Matematičeskie zametki, Tome 78 (2005) no. 5, pp. 710-717.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that the Fano surface which parameterizes the set of straight lines on a real $M$-threefold of degree 3 is also an $M$-surface. The converse statement is also true. The proof is based on the results about the intermediate Jacobian of a complex cubic threefold due to C. Clemens and P. Griffiths. 
@article{MZM_2005_78_5_a6,
     author = {V. A. Krasnov},
     title = {On the {Fano} {Surface} of a {Real} {Cubic} $M${-Threefold}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {710--717},
     publisher = {mathdoc},
     volume = {78},
     number = {5},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_5_a6/}
}
TY  - JOUR
AU  - V. A. Krasnov
TI  - On the Fano Surface of a Real Cubic $M$-Threefold
JO  - Matematičeskie zametki
PY  - 2005
SP  - 710
EP  - 717
VL  - 78
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_78_5_a6/
LA  - ru
ID  - MZM_2005_78_5_a6
ER  - 
%0 Journal Article
%A V. A. Krasnov
%T On the Fano Surface of a Real Cubic $M$-Threefold
%J Matematičeskie zametki
%D 2005
%P 710-717
%V 78
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2005_78_5_a6/
%G ru
%F MZM_2005_78_5_a6
V. A. Krasnov. On the Fano Surface of a Real Cubic $M$-Threefold. Matematičeskie zametki, Tome 78 (2005) no. 5, pp. 710-717. http://geodesic.mathdoc.fr/item/MZM_2005_78_5_a6/

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

[2] Grotendik A., O nekotorykh voprosakh gomologicheskoi algebry, IL, M., 1961

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

[4] Krasnov V. A., “Kharakteristicheskie klassy vektornykh rassloenii na veschestvennom algebraicheskom mnogoobrazii”, Izv. AN SSSR. Ser. matem., 55:4 (1991), 716–746 | MR

[5] Krasnov V. A., “Algebraicheskie tsikly na veschestvennom algebraicheskom $GM$-mnogoobrazii i ikh prilozheniya”, Izv. RAN. Ser. matem., 57:4 (1993), 153–173 | MR | Zbl

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

[7] Krasnov V. A., “Ekvivariantnye kogomologii veschestvennoi algebraicheskoi poverkhnosti i ikh prilozheniya”, Izv. RAN. Ser. matem., 60:6 (1996), 101–126 | Zbl

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