## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Fano threefolds with wild conic bundle structures

#### Abstract

We classify smooth Fano threefolds with wild conic bundle structures in characteristic 2 without using the general classification methods of Fano threefolds. General results on wild hypersurface bundles of degree $p$ are also obtained.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 79, Number 6 (2003), 111-114.

Dates
First available in Project Euclid: 18 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116443691

Digital Object Identifier
doi:10.3792/pjaa.79.111

Mathematical Reviews number (MathSciNet)
MR1992032

Zentralblatt MATH identifier
1058.14058

Subjects
Primary: 14J45: Fano varieties
Secondary: 14E30: Minimal model program (Mori theory, extremal rays)

#### Citation

Mori, Shigefumi; Saito, Natsuo. Fano threefolds with wild conic bundle structures. Proc. Japan Acad. Ser. A Math. Sci. 79 (2003), no. 6, 111--114. doi:10.3792/pjaa.79.111. https://projecteuclid.org/euclid.pja/1116443691

#### References

• Kollár, J.: Extremal rays on smooth threefolds, (characteristic $p$). Ann. Scient. Ec. Sup. 4e serie, 24, 339–361 (1991).
• Mori, S.: Threefolds whose canonical bundles are not numerically effective. Ann. Math., 116, 133–176 (1982).
• Mori, S., and Mukai, S.: Classification of Fano 3-folds with $B_2\ge 2$. Manuscripta Math., 36, 147–162 (1981); Erratum. Classification of Fano 3-folds with $B_2\ge 2$. Manuscipta Math., 110, 407 (2003).
• Mori, S., and Mukai, S.: On Fano 3-folds with $B_2\ge 2$. Advanced Studies in Pure Mathematics, vol.,1, Kinokuniya, Tokyo, and North-Holland, Amsterdam, pp. 101–129 (1983).
• Mori, S., and Mukai, S.: Classification of Fano 3-folds with $B_2\ge 2$, I. Algebraic and Topological Theories – To the Memory of Dr. Takehiko Miyata (eds. Nagata, M. et al.). Kinokuniya, Tokyo, pp. 496–545 (1986).
• Saito, N.: Fano threefolds with Picard number 2 in positive characteristic. Kodai Math. J. (To appear).
• Shepherd-Barron, N. I.: Fano threefolds in positive characteristic. Compositio Math., 105, 237–265 (1997).
• Takeuchi, K.: Some birational maps of Fano 3-folds. Compositio Math., 71, 265–283 (1989).