Mathematics – Algebraic Geometry
Scientific paper
2008-01-20
Mathematics
Algebraic Geometry
23 pages. changed the exposition of the previous version
Scientific paper
A normal projective complex surface is called a rational homology projective plane if it has the same Betti numbers with the complex projective plane $\mathbb{C}\mathbb{P}^2$. It is known that a rational homology projective plane with quotient singularities has at most 5 singular points. So far all known examples have at most 4 singular points. In this paper, we prove that a rational homology projective plane $S$ with quotient singularities such that $K_S$ is nef has at most 4 singular points except one case. The exceptional case comes from Enriques surfaces with a configuration of 9 smooth rational curves whose Dynkin diagram is of type $ 3A_1 \oplus 2A_3$. We also obtain a similar result in the differentiable case and in the symplectic case under certain assumptions which all hold in the algebraic case.
Hwang DongSeon
Keum JongHae
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