摘要翻译：
本文继续研究满足K_s^2<3chi(S)的一般S型极小曲面的代数基元群。证明了如果K_s^2=3\chi(S)-1且S的代数基本群为8阶，则S是Campedelli曲面。根据Math.AG/0512483和Math.AG/0605733的结果，这表明K^2<3\chi的曲面的基本群最多有9级，如果有8级或9级，则S是Campedelli曲面。为了得到这一结果，我们对一般类型的极小曲面建立了一些分类结果，使得K^2=3P_g-5和规范映射是双分态射。我们还研究了具有Z2^3-作用的有理曲面。
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英文标题：
《Surfaces with K^2<3\chi and finite fundamental group》
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作者：
Ciro Ciliberto, Margarida Mendes Lopes and Rita Pardini
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  In this paper we continue the study of algebraic fundamentale group of minimal surfaces of general type S satisfying K_S^2<3\chi(S). We show that, if K_S^2= 3\chi(S)-1 and the algebraic fundamental group of S has order 8, then S is a Campedelli surface.   In view of the results of math.AG/0512483 and math.AG/0605733, this implies that the fundamental group of a surface with K^2<3\chi that has no irregular etale cover has order at most 9, and if it has order 8 or 9, then S is a Campedelli surface.   To obtain this result we establish some classification results for minimal surfaces of general type such that K^2=3p_g-5 and such that the canonical map is a birational morphism. We also study rational surfaces with a Z_2^3-action.
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PDF链接：
https://arxiv.org/pdf/0706.1784