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摘要翻译：
本文研究带标记点的黎曼曲面上（非强）抛物Higgs束模空间的几何性质。将Atiyah代数对偶上的Poisson结构推广到抛物向量丛的模空间上，证明了该空间具有Poisson结构。通过考虑满标志的情况，我们得到了所有其它标志类型的Grothendieck-Springer分辨率，特别是对扭曲Higgs束模空间的Grothendieck-Springer分辨率，正如Markman和Bottacin所研究的，并用于Laumon-Ng\o最近的工作中。我们讨论了Hitchin系统，证明了所有这些模空间都是泊松意义下的可积系统。
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英文标题：
《Moduli of Parabolic Higgs Bundles and Atiyah Algebroids》
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作者：
Marina Logares and Johan Martens
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最新提交年份：
2010
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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：Symplectic Geometry 辛几何
分类描述：Hamiltonian systems, symplectic flows, classical integrable systems
哈密顿系统，辛流，经典可积系统
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一级分类：Physics 物理学
二级分类：Exactly Solvable and Integrable Systems 精确可解可积系统
分类描述：Exactly solvable systems, integrable PDEs, integrable ODEs, Painleve analysis, integrable discrete maps, solvable lattice models, integrable quantum systems
精确可解系统，可积偏微分方程，可积偏微分方程，Painleve分析，可积离散映射，可解格模型，可积量子系统
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英文摘要：
In this paper we study the geometry of the moduli space of (non-strongly) parabolic Higgs bundles over a Riemann surface with marked points. We show that this space possesses a Poisson structure, extending the one on the dual of an Atiyah algebroid over the moduli space of parabolic vector bundles. By considering the case of full flags, we get a Grothendieck-Springer resolution for all other flag types, in particular for the moduli spaces of twisted Higgs bundles, as studied by Markman and Bottacin and used in the recent work of Laumon-Ng\^o. We discuss the Hitchin system, and demonstrate that all these moduli spaces are integrable systems in the Poisson sense.
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PDF链接：
https://arxiv.org/pdf/0811.0817
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