摘要翻译：
设M_0^r为光滑实三次曲面的模空间。我们证明了它的每一个分量都允许一个真正的双曲结构。更准确地说，我们可以从实双曲空间H^4中去掉一些低维的测地线子空间，通过算术群形成商，得到与模空间的一个分量同构的轨道。有五个组成部分。对于每一个，我们在PO(4,1）中描述了相应的格。我们还得到了关于M_0^R拓扑的几个新的和几个旧的结果。设M_s^r是在几何不变理论意义上稳定的实三次曲面的模空间。我们证明了这个空间包含一个双曲结构，它对m_0^r的限制是刚才提到的。PO(4,1）中对应的格是非算术的，我们为它找到了一个显式的基本区域。
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英文标题：
《Hyperbolic geometry and moduli of real cubic surfaces》
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作者：
Daniel Allcock, James A. Carlson and Domingo Toledo
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最新提交年份：
2009
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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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一级分类：Mathematics        数学
二级分类：Group Theory        群论
分类描述：Finite groups, topological groups, representation theory, cohomology, classification and structure
有限群、拓扑群、表示论、上同调、分类与结构
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英文摘要：
  Let M_0^R be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space H^4 and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in PO(4,1). We also derive several new and several old results on the topology of M_0^R. Let M_s^R be the moduli space of real cubic surfaces that are stable in the sense of geometric invariant theory. We show that this space carries a hyperbolic structure whose restriction to M_0^R is that just mentioned. The corresponding lattice in PO(4,1), for which we find an explicit fundamental domain, is nonarithmetic.
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PDF链接：
https://arxiv.org/pdf/0707.1058