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摘要翻译：
Crawley-Boevey和Shaw最近介绍了变形预射影代数的一个乘法模拟，他们称之为乘法预射影代数。本文研究了这类代数的（半）稳定表示的模空间（乘法颤簇），它实际上与颤簇有许多相似之处。我们证明了颤簇的幂零子簇与乘法颤簇的幂零子簇之间存在复解析同构（可推广为这些管状邻域之间的辛明天）。我们还证明了当颤振为星形时，乘法颤振变化使Simpson（poly）稳定滤波局域系统参数化，并给出了给定的滤波类型、权值和每个穿刺点周围相应的梯度局域系统。
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英文标题：
《Geometry of Multiplicative Preprojective Algebra》
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作者：
Daisuke Yamakawa
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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：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：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：
Crawley-Boevey and Shaw recently introduced a certain multiplicative analogue of the deformed preprojective algebra, which they called the multiplicative preprojective algebra. In this paper we study the moduli space of (semi)stable representations of such an algebra (the multiplicative quiver variety), which in fact has many similarities to the quiver variety. We show that there exists a complex analytic isomorphism between the nilpotent subvariety of the quiver variety and that of the multiplicative quiver variety (which can be extended to a symplectomorphism between these tubular neighborhoods). We also show that when the quiver is star-shaped, the multiplicative quiver variety parametrizes Simpson's (poly)stable filtered local systems on a punctured Riemann sphere with prescribed filtration type, weight and associated graded local system around each puncture.
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PDF链接：
https://arxiv.org/pdf/0710.2649
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