Geodesic
Del Pezzo Surfaces with Log Terminal Singularities
Matematičeskie zametki, Tome 83 (2008) no. 2, pp. 170-180.

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We prove that there are no del Pezzo surfaces with five log terminal singularities and the Picard number 1. In the course of the proof, we make use of fibrations with general fiber $\mathbb P^1$.
Mots-clés : algebraic surface, del Pezzo surface
Keywords: log terminal singularity, anticanonical class, Picard number, canonical divisor, ruled surface. 
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G. N. Belousov. Del Pezzo Surfaces with Log Terminal Singularities. Matematičeskie zametki, Tome 83 (2008) no. 2, pp. 170-180. http://geodesic.mathdoc.fr/item/MZM_2008_83_2_a1/

[1] Y. Kawamata, K. Matsuda, J. Matsuki, “Introduction to the minimal model program”, Algebraic Geometry, Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987, 283–360 | MR | Zbl

[2] M. Furushima, “Singular del Pezzo surfaces and analytic compactifications of $3$-dimensional complex affine space $C^3$”, Nagoya Math. J., 104 (1986), 1–28 | MR | Zbl

[3] M. Miyanishi, D.-Q. Zhang, “Gorenstein log del Pezzo surfaces of rank one”, J. Algebra, 118:1 (1988), 63–84 | DOI | MR | Zbl

[4] H. Kojima, “Logarithmic del Pezzo surfaces of rang one with unique singular points”, Japan. J. Math. (N.S.), 25:2 (1999), 343–375 | MR | Zbl

[5] V. A. Alekseev, V. V. Nikulin, “Klassifikatsiya poverkhnostei del Petstso s log-terminalnymi osobennostyami indeksa $\le2$, involyutsii na poverkhnostyakh $K3$ i gruppy otrazhenii v prostranstvakh Lobachevskogo”, Doklady po matematike i ee prilozheniyam, t. 2, vyp. 2, Matem. in-t im. V. A. Steklova AN SSSR, Moskva–Tula, 1988, 51–150 | MR

[6] S. Keel, J. McKernan, Rational Curves on Quasi-projective Surfaces, Mem. Amer. Math. Soc., 140{, 669}, Amer. Math. Soc., Providence, RI, 1999 | MR | Zbl

[7] J. Kollar, Is there a topological Bogomolov–Miyaoka–Yau inequality?, arXiv: math/0602562

[8] Y. Kawamata, “Crepant blowing-up of $3$-dimensional canonical singularities and its application to degenerations of surfaces”, Ann. of Math. (2), 127:1 (1988), 93–163 | DOI | MR | Zbl

[9] D.-Q. Zhang, “Logarithmic del Pezzo surfaces one with rational double and triple singular points”, Tohoku Math. J. (2), 41:3 (1989), 399–452 | DOI | MR | Zbl

[10] E. Brieskorn, “Rationale Singularitäten komplexer Flächen”, Invent. Math., 4:5 (1968), 336–358 | DOI | MR | Zbl

[11] A. I. Iliev, “Log-terminalnye osobennosti algebraicheskikh poverkhnostei”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1986, no. 3, 38–44 | MR | Zbl

[12] D.-Q. Zhang, “Logarithmic del Pezzo surfaces of rang one with contractible boundaries”, Osaka J. Math., 25:2 (1988), 461–497 | MR | Zbl