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摘要翻译：
R.Rim\'anyi将两个奇点X和Y的关联类定义为$[X]_Y$,这是X的Thom多项式对Y的限制。他猜想（在温和的条件下）关联不为零当且仅当Y在X的闭包内。推广这一概念，我们定义了一个表示的两个轨道X和Y的关联类。我们给出了Y具有关联类$[X]_Y$不为零的充分条件（正性）当且仅当Y对于任何其它轨道X处于X的闭包中。我们证明了对于许多有趣的情形，例如Dynkin型正性的颤动表示对于所有轨道都成立。换句话说，在这些情况下，关联类完全决定了轨道的层次结构。我们还研究了正性并非对所有轨道都成立的奇点的情况。
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英文标题：
《The incidence class and the hierarchy of orbits》
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作者：
L\'aszl\'o M. Feh\'er, Zsolt Patakfalvi
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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：Algebraic Topology 代数拓扑
分类描述：Homotopy theory, homological algebra, algebraic treatments of manifolds
同伦理论，同调代数，流形的代数处理
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英文摘要：
R. Rim\'anyi defined the incidence class of two singularities X and Y as $[X]|_Y$, the restriction of the Thom polynomial of X to Y. He conjectured that (under mild conditions) the incidence is not zero if and only if Y is in the closure of X. Generalizing this notion we define the incidence class of two orbits X and Y of a representation. We give a sufficient condition (positivity) for Y to have the property that the incidence class $[X]|_Y$ is not zero if and only if Y is in the closure of X for any other orbit X. We show that for many interesting cases, e.g. the quiver representations of Dynkin type positivity holds for all orbits. In other words in these cases the incidence classes completely determine the hierarchy of the orbits. We also study the case of singularities where positivity doesn't hold for all orbits.
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PDF链接：
https://arxiv.org/pdf/0705.3834
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