Classification of log del Pezzo surfaces of index three. (English) Zbl 1375.14121

Fujita, Kento; Yasutake, Kazunori

J. Math. Soc. Japan 69, No. 1, 163-225 (2017).

A log Del Pezzo surface is a normal projective surface \(X\) with log terminal singularities such that \(-K_X\) is ample. The index of \(X\) is the smallest positive integer \(r\) such that \(rK_X\) is Cartier. Log Del Pezzo surfaces naturally appear as fibers of three dimensional Fano-Mori fibrations \(\mathcal{X}\rightarrow T\), where \(T\) is a smooth curve.
Log Del Pezzo surfaces of index 1 have been classified by V. A. Alekseev and V. V. Nikulin [Sov. Math., Dokl. 39, No. 3, 507–511 (1989; Zbl 0705.14038); translation from Dokl. Akad. Nauk SSSR 306, No. 3, 525–528 (1989)] and log Del Pezzo surfaces of index 2 have been classified by N. Nakayama [J. Math. Sci., Tokyo 14, No. 3, 293–498 (2007; Zbl 1175.14029)].
In this paper the author uses the method developed by Nakayama in [loc. cit.] in order to classify log Del Pezzo surfaces of index 3.

Reviewer: Nikolaos Tziolas (Nicosia)

MSC:

14J26	Rational and ruled surfaces
14E30	Minimal model program (Mori theory, extremal rays)

Keywords:

Del Pezzo surfaces; log terminal singularities; index 3

Citations:

Zbl 0705.14038; Zbl 1175.14029