Some conic bundles

I. Yu. Fedorov

Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 903-910.

Résumé

A representation of the anticanonical K3 surface of a singular pencil of conics is described. This generalizes the well-known Shokurov theorem.

Bibliographie

[1] Mori S., “Flip theorem and the existence of minimal models for 3-folds”, J. Amer. Math. Soc., 1 (1988), 117–253 | DOI | MR | Zbl

[2] Iskovskikh V. A., Lektsii po trekhmernym algebraicheskim mnogoobraziyam: Mnogoobraziya Fano, Izd-vo MGU, M., 1988 | Zbl

[3] Shokurov V. V., “Gladkost obschego antikanonicheskogo divizora na mnogoobraziyakh Fano”, Izv. AN SSSR. Ser. matem., 43 (1979), 430–441 | MR | Zbl

[4] Prokhorov Yu. G., “O trekhmernykh mnogoobraziyakh s giperploskimi secheniyami – poverkhnostyami Enrikvesa”, Matem. sb., 186:9 (1995), 113–124 | MR | Zbl

[5] Reid M., Projective Morphism According to Kawamata, Preprint, Warwick, 1983

[6] Klemens Kh., Kollar Ya., Mori S., Mnogomernaya kompleksnaya geometriya, Mir, M., 1993

[7] Kawamata Y., Matsuda K., Matsuki K., “Introduction to the minimal model problem”, Algebraic Geometry, Proc. Symp. (Sendai, 1985), Adv. Stud. Pure Math., 10, Kinokuniya, Tokyo, 1987, 283–360 | MR

[8] Alexeev V., “General elephants of $\mathbb Q$-Fano 3-folds”, Compositio Math., 91:1 (1994), 91–116 | MR | Zbl

[9] Alexeev V. A., “Theorems about good divisors on log Fano varieties (case of index $r>n-2$)”, Algebraic Geometry, Proc. US–USSR Symp. (1989), Lecture Notes in Math., 1479, Springer, Chicago, IL, 1991, 1–9 | MR