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Algebraic surfaces with nef and big anti-canonical divisor

Published online by Cambridge University Press:  24 October 2008

D.-Q. Zhang
D.-Q. Zhang
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 0511. E-mail: MATZDQ©NUSVM.BITNET
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Extract

Let S be a normal projective algebraic surface over C with at worst quotient singularities. S is a quasi-log del Pezzo surface if the anti-canonical divisor — Ks is nef (= numerically effective) and big, i.e. — Ks. C ≥ 0 for all curves C on S and (−Ks)2 > 0. Further, if — Ks is ample we say S is a log del Pezzo surface.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 1 , January 1995 , pp. 161 - 163
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

REFERENCES

[1]Brieskorn, E.. Rationale Singularitäten komplexer Flächen. Invent. Math. 4 (1968), 336–358.CrossRefGoogle Scholar
[2]Chau, T. C.. A note concerning Fox's paper on Fenchel's conjecture. Proc. Amer.Math. Soc. 88 (1983), 584–586.Google Scholar
[3]Fox, R. H.. On Fenchel's conjecture about F-groups. Math. Tidsskr. B (1952), 61–65.Google Scholar
[4]Fujiki, A., Kobayashi, R. and Lu, S.. On the Fundamental Group of Certain Open Normal Surfaces. Saitama Math. J. 11 (1993), 15–20.Google Scholar
[5]Gurjar, R. V. and Zhang, D.-Q., π1 of smooth points of a log del Pezzo surface is finite: I, II, to appear in J. Math. Sci. Univ. Tokyo.Google Scholar
[6]Kawamata, Y., Matsuda, K. and Matsuki, K.. Introduction to the minimal model problem. In Algebraic Geometry, Sendai, 1985, Advanced Studies in Pure Mathematics, Vol. 10 (Kinokuniya-North-Holland, 1987), pp. 283–360.CrossRefGoogle Scholar
[7]Nori, M. V.. Zariski's conjecture and related problems. Ann. Sci. École Norm. Sup. 16 (1983), 305–344.CrossRefGoogle Scholar
[8]Sakai, F.. Anti-Kodaira Dimension of Ruled Surfaces. Sci. Rep. Saitama Univ. X, 2 (1982), 1–7.Google Scholar
[9]Zhang, D.-Q.. Normal algebraic surfaces of anti-Kodaira dimension two (preprint 1993).Google Scholar
[10]Zhang, D.-Q.. Algebraic surfaces with log canonical singularites and the fundamental groups of their smooth parts (preprint 1994).Google Scholar
[11]Zhang, D.-Q.. The fundamental group of the smooth part of a log Fano variety (preprint 1993).Google Scholar