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

Margarida Mendes Lopes·Rita Pardini
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Abstract

We study the structure of the algebraic fundamental group for minimal surfaces of general type S satisfying K_S^2<=3χ-2$ and not having any irregular etale cover. We show that, if K_S^2<=3χ-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<= 3χ-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<=χ<=4, K^2=3χ-3 and these possibilities do occur.

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Margarida Mendes Lopes, Rita Pardini. 2006-05-29. The order of finite algebraic fundamental groups of surfaces with K^2<=3χ-2. https://arxiv.org/abs/math/0605733

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