摘要翻译：
带标记点的实亏格零代数曲线模空间的可定向覆盖是由结合面体平铺的紧非球面流形，解决了系统树空间的奇异性。分辨率将平面度量树映射到其底层的抽象代表，将模空间的显式几何分解折叠成立方体。这种分解赋予分解空间一个有趣的规范伪度量。本文的第二部分定义了实二次型空间的相关（stacky）分辨率，并建议，也许没有太多的理由，由这些对象参数化的振子系统可以提供基因组学中的有用模型。
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英文标题：
《Diagonalizing the genome I: navigation in tree spaces》
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作者：
Satyan L. Devadoss, Jack Morava
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最新提交年份：
2012
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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：Geometric Topology        几何拓扑
分类描述：Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
流形，轨道，多面体，细胞复合体，叶状，几何结构
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一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  The orientable cover of the moduli space of real genus zero algebraic curves with marked points is a compact aspherical manifold tiled by associahedra, which resolves the singularities of the space of phylogenetic trees. The resolution maps planar metric trees to their underlying abstract representatives, collapsing and folding an explicit geometric decomposition of the moduli space into cubes. This decomposition endows the resolving space with an interesting canonical pseudometric.   The second part of this paper defines a related (stacky) resolution of a space of real quadratic forms, and suggests, perhaps without much justification, that systems of oscillators parametrized by such objects may provide useful models in genomics.
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PDF链接：
https://arxiv.org/pdf/1009.3224