The order of finite algebraic fundamental groups of surfaces with K^2<=3χ-2

Details The order of finite algebraic fundamental groups of surfaces with K^2<=3χ-2 The order of finite algebraic fundamental groups of surfaces with K^2<=3χ-2

2006-05-29

arxiv.org/abs/math/0605733v1

Mathematics

Algebraic Geometry

To appear in the volume ''Algebraic geometry and Topology" Suurikaiseki kenkyusho Koukyuuroku, No. 1490 (2006), pp. 69--75

Scientific paper

We study the structure of the algebraic fundamental group for minimal surfaces of general type S satisfying K_S^2<=3\chi-2$ and not having any irregular etale cover. We show that, if K_S^2<=3\chi-2, then then the algebraic fundamental group of S has order at most 5, and equality only occurs if S is a Godeaux surface. We also show that if K_S^2<= 3\chi-3 and the algebraic fundamental group of S is not trivial, then it is Z_2, or Z_2^2 or Z_3. Furthermore in this last case one has: 2<=\chi<=4, K^2=3\chi-3 and these possibilities do occur.

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