广义Burniat型曲面与Bagnera-de Franchis簇
Generalized Burniat type surfaces and Bagnera-de Franchis varieties
摘要：
本文构造了3个新的p_g = q = 0，K^2 = 6的一般型曲面族和7个新的p_g = q = 1，K^2 = 6的一般型曲面族，实现了10个新的基本群.我们还表明，这些家庭对应于两两不同的不可约连通分量的Gieseker模空间的一般类型的表面。我们使用两种不同的主要成分来实现这一点。首先，我们引入一类新的曲面，称为广义Burniat型曲面，我们完全分类他们（和连通的成分的模空间包含他们）。其次，我们介绍的概念Bagnera-de Franchis品种：这些是自由的阿贝尔簇的循环群（不包括只有翻译）。对于这些，我们开发一些基本的结果。
英文摘要：
In this article we construct three new families of surfaces of general type with p_g = q = 0,K^2 = 6, and seven new families of surfaces of general type with p_g = q = 1, K^2 = 6, realizing 10 new fundamental groups. We also show that these families correspond to pairwise distinct irreducible connected components of the Gieseker moduli space of surfaces of general type. We achieve this using two different main ingredients. First we introduce a new class of surfaces, called generalized Burniat type surfaces, and we completely classify them (and the connected com- ponents of the moduli space containing them). Second, we introduce the notion of Bagnera-de Franchis varieties: these are the free quotients of an Abelian variety by a cyclic group (not consisting only of translations). For these we develop some basic results.
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