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摘要翻译：
引入了沿超曲面奇点的对数向量场初始项的李代数。推广[GS06,THM.5.4]中的形式结构定理，我们证明了它的线性投影的完全可约部分形式上提升为一个对数向量场的线性李代数。对于拟齐次奇点，我们证明了这种线性化的收敛性。我们将我们的构造与Hauser和M'Uller[M'Ul86,HM89]关于奇点自同构群的Levi子群的工作联系起来，证明了即使对于代数奇点也是收敛的。在初始李代数的基础上，引入了约化超曲面奇性的概念，并证明了任何约化自由因子都是线性的。作为应用，我们利用超曲面奇点的初始李代数的半单部分，给出了超曲面奇点维数的一个下界。
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英文标题：
《Initial logarithmic Lie algebras of hypersurface singularities》
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作者：
Michel Granger and Mathias Schulze
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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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英文摘要：
We introduce a Lie algebra of initial terms of logarithmic vector fields along a hypersurface singularity. Extending the formal structure theorem in [GS06, Thm. 5.4], we show that the completely reducible part of its linear projection lifts formally to a linear Lie algebra of logarithmic vector fields. For quasihomogeneous singularities, we prove convergence of this linearization. We relate our construction to the work of Hauser and M"uller [M"ul86, HM89] on Levi subgroups of automorphism groups of singularities, which proves convergence even for algebraic singularities. Based on the initial Lie algebra, we introduce a notion of reductive hypersurface singularity and show that any reductive free divisor is linear. As an application, we describe a lower bound for the dimension of hypersurface singularities in terms of the semisimple part of their initial Lie algebra.
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PDF链接：
https://arxiv.org/pdf/0807.1916
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