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Algebraic surfaces with log canonical singularities and the fundamental groups of their smooth parts


Author: D.-Q. Zhang
Journal: Trans. Amer. Math. Soc. 348 (1996), 4175-4184
MSC (1991): Primary 14J45; Secondary 14E20, 14J26, 14J17
DOI: https://doi.org/10.1090/S0002-9947-96-01595-4
MathSciNet review: 1348158
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Abstract: Let $(S, \Delta )$ be a log surface with at worst log canonical singularities and reduced boundary $\Delta $ such that $-(K_{S}+\Delta )$ is nef and big. We shall prove that $S^{o} = S - Sing S - \Delta $ either has finite fundamental group or is affine-ruled. Moreover, $\pi _{1}(S^{o})$ and the structure of $S$ are determined in some sense when $\Delta = 0$.


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Additional Information

D.-Q. Zhang
Affiliation: Department of Mathematics, National University of Singapore, Singapore
Email: matzdq@nus.sg

DOI: https://doi.org/10.1090/S0002-9947-96-01595-4
Keywords: Log canonical singularity, nef and big anti-canonical divisor, fundamental group, affine-ruledness
Received by editor(s): February 25, 1995
Received by editor(s) in revised form: June 9, 1995
Article copyright: © Copyright 1996 American Mathematical Society

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