论文标题
理查森细胞的Chern-Schwartz-Macpherson类的猜想阳性
Conjectural positivity of Chern-Schwartz-MacPherson classes for Richardson cells
论文作者
论文摘要
经过Aluffi-Mihalcea-Schürmann-Su的一些工作，用于舒伯特细胞的CSM类，以及R. Rimanyi和L. Mihalcea的一些精心计算机计算，我推测，Schubert基础表达的Richardson细胞的CSM类别具有非维持系数。该猜想主要是由新产品$ \ square $来自Segre类别的Flag品种共同体（因此，该产品的相关GR是标准杯产品）以及标准Schubert基础标准schubert基础基本的结构$ \ Square $具有交替的标志行为的猜想。我证明，$ \ square $的结构常数符号的这种猜想将从我上述阳性构想中，涉及Richardson细胞的CSM类别。
Following some work of Aluffi-Mihalcea-Schürmann-Su for the CSM classes of Schubert cells and some elaborate computer calculations by R. Rimanyi and L. Mihalcea, I conjecture that the CSM classes of the Richardson cells expressed in the Schubert basis have nonnegative coefficients. This conjecture was principally motivated by a new product $\square$ coming from the Segre classes in the cohomology of flag varieties (such that the associated Gr of this product is the standard cup product) and the conjecture that the structure constants of this new product $\square$ in the standard Schubert basis have alternating sign behavior. I prove that this conjecture on the sign of the structure constants of $\square$ would follow from my above positivity conjecture about the CSM classes of Richardson cells.
