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摘要翻译：
本文研究了箭囊圈的Grothendieck类，即箭囊表示空间的不变闭子簇。对于无定向环的颤振，我们证明了颤振循环的类别是由颤振系数决定的，这推广了前人研究的等定向a型颤振的颤振系数。我们猜想颤振系数满足正性和有限性的性质。我们的主要结果是Dynkin型有理奇点轨道闭包的颤振系数公式，证实了有限猜想。这个公式是基于Reineke对这种轨道封闭的去模糊化。对于A3型颤振，我们给出了颤振系数的正的组合公式，证实了完全猜想。我们还将箭颤系数解释为由向量丛映射的箭颤定义的简并轨迹的公式。
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英文标题：
《Quiver coefficients of Dynkin type》
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作者：
Anders Skovsted Buch
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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：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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一级分类：Mathematics 数学
二级分类：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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英文摘要：
We study the Grothendieck classes of quiver cycles, i.e. invariant closed subvarieties of the representation space of a quiver. For quivers without oriented loops we show that the class of a quiver cycle is determined by quiver coefficients, which generalize the earlier studied quiver coefficients for equioriented quivers of type A. We conjecture that quiver coefficients satisfy positivity and finiteness properties. Our main result is a formula for the quiver coefficients for orbit closures of Dynkin type with rational singularities, which confirms the finiteness conjecture. This formula is based on Reineke's desingularization of such orbit closures. For quivers of type A3, we give positive combinatorial formulas for the quiver coefficients, which confirm the full conjecture. We also interpret quiver coefficients as formulas for degeneracy loci defined by quivers of vector bundle maps.
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PDF链接：
https://arxiv.org/pdf/0708.3418
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