摘要翻译：
正则半单Hessenberg簇是在数论、数值分析、表示论、代数几何和组合学中出现的标志簇的子簇。我们给出了用Chern类表示正则半单Hessenberg变体类的Giambelli公式。事实上，我们证明了每一个正则半单Hessenberg簇的上同调类都是某种双Schubert多项式的特化，并对这种特化给出了自然的几何解释。我们还利用旗形上同调环的Schubert基对这类进行了分解。得到的系数是非负的，并给出了在许多情况下系数的闭合组合公式。我们引入了一个密切相关的格式族，称为正则幂零Hessenberg格式，并利用我们的结果来确定这类格式何时被约简。
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英文标题：
《Schubert polynomials and classes of Hessenberg varieties》
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作者：
Dave Anderson, Julianna Tymoczko
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最新提交年份：
2008
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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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英文摘要：
  Regular semisimple Hessenberg varieties are a family of subvarieties of the flag variety that arise in number theory, numerical analysis, representation theory, algebraic geometry, and combinatorics. We give a "Giambelli formula" expressing the classes of regular semisimple Hessenberg varieties in terms of Chern classes. In fact, we show that the cohomology class of each regular semisimple Hessenberg variety is the specialization of a certain double Schubert polynomial, giving a natural geometric interpretation to such specializations. We also decompose such classes in terms of the Schubert basis for the cohomology ring of the flag variety. The coefficients obtained are nonnegative, and we give closed combinatorial formulas for the coefficients in many cases. We introduce a closely related family of schemes called regular nilpotent Hessenberg schemes, and use our results to determine when such schemes are reduced.
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PDF链接：
https://arxiv.org/pdf/0710.3182