摘要翻译：
Fialowski和Schlichenmaier构造了向量场李代数的全局变形的例子。我们以一种概念性的方式来制定他们的方法。也就是说，我们构造了一个变形叠加和一个态射，形成了稳定标记曲线的模叠加。该态射与一个标记曲线族相关联，该标记曲线族是由提取标记点的族上的垂直向量场的李代数得到的李代数族。我们用Pursell-Shanks理论证明了这个态射几乎是一个单态射。
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英文标题：
《Deformations of Lie algebras of vector fields arising from families of
  schemes》
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作者：
Friedrich Wagemann (LMJL)
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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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一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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英文摘要：
  Fialowski and Schlichenmaier constructed examples of global deformations of Lie algebras of vector fields from deforming the underlying variety. We formulate their approach in a conceptual way. Namely, we construct a stack of deformations and a morphism form the moduli stack of stable marked curves. The morphism associates to a family of marked curves the family of Lie algebras obtained by taking the Lie algebra of vertical vector fields on the family where one has extracted the marked points. We show that this morphism is almost a monomorphism by Pursell-Shanks theory.
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PDF链接：
https://arxiv.org/pdf/0707.4054