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

Zhang, D.-Q.

doi:10.1090/S0002-9947-96-01595-4

Algebraic surfaces with log canonical singularities and the fundamental groups of their smooth parts
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by D.-Q. Zhang PDF

Trans. Amer. Math. Soc. 348 (1996), 4175-4184 Request permission

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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