族的向量場李代數(shù)的變形 方案

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摘要翻譯：
Fialowski和Schlichenmaier構(gòu)造了向量場李代數(shù)的全局變形的例子。我們以一種概念性的方式來制定他們的方法。也就是說，我們構(gòu)造了一個變形疊加和一個態(tài)射，形成了穩(wěn)定標(biāo)記曲線的模疊加。該態(tài)射與一個標(biāo)記曲線族相關(guān)聯(lián)，該標(biāo)記曲線族是由提取標(biāo)記點的族上的垂直向量場的李代數(shù)得到的李代數(shù)族。我們用Pursell-Shanks理論證明了這個態(tài)射幾乎是一個單態(tài)射。
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英文標(biāo)題：
《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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分類信息：

一級分類：Mathematics        數(shù)學(xué)
二級分類：Algebraic Geometry        代數(shù)幾何
分類描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代數(shù)簇，疊，束，格式，模空間，復(fù)幾何，量子上同調(diào)
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一級分類：Physics        物理學(xué)
二級分類：Mathematical Physics        數(shù)學(xué)物理
分類描述：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
這一類別的文章集中在說明數(shù)學(xué)在物理問題中的應(yīng)用的研究領(lǐng)域，為這類應(yīng)用開發(fā)數(shù)學(xué)方法，或提供現(xiàn)有物理理論的數(shù)學(xué)嚴(yán)格公式。提交的數(shù)學(xué)-PH應(yīng)該對物理方向的數(shù)學(xué)家和數(shù)學(xué)方向的物理學(xué)家都感興趣；主要對理論物理學(xué)家或數(shù)學(xué)家感興趣的投稿可能應(yīng)該指向各自的物理/數(shù)學(xué)類別
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一級分類：Mathematics        數(shù)學(xué)
二級分類：Mathematical Physics        數(shù)學(xué)物理
分類描述：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的別名。這一類別的文章集中在說明數(shù)學(xué)在物理問題中的應(yīng)用的研究領(lǐng)域，為這類應(yīng)用開發(fā)數(shù)學(xué)方法，或提供現(xiàn)有物理理論的數(shù)學(xué)嚴(yán)格公式。提交的數(shù)學(xué)-PH應(yīng)該對物理方向的數(shù)學(xué)家和數(shù)學(xué)方向的物理學(xué)家都感興趣；主要對理論物理學(xué)家或數(shù)學(xué)家感興趣的投稿可能應(yīng)該指向各自的物理/數(shù)學(xué)類別
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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鏈接：
https://arxiv.org/pdf/0707.4054

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關(guān)鍵詞：Mathematical Applications formulations mathematica mathematics family 證明 deformations 提取 代數(shù)