论文标题
Castelnuovo-Mumford的阶梯决定性品种的规律性和格拉斯曼舒伯特品种的斑块
Castelnuovo-Mumford regularity of ladder determinantal varieties and patches of Grassmannian Schubert varieties
论文作者
论文摘要
我们为Grothendieck多项式提供了学位公式，该多项式由Vexillary排列和1432美元的$ 1432 $ - 通过Tableau Combinatorics进行避免排列。这些公式概括了一个对称性Grothendieck多项式的公式，该公式出现在作者与Y. Ren和A. St. Dizier的先前联合作品中。 我们将公式用于计算一类普遍的确定性理想类别的Castelnuovo-Mumford规律性。特别是，我们为所有单面混合梯子决定理想的规律性提供了组合公式。我们还为某些Kazhdan-Lusztig理想的规律性提供了公式，包括来自格拉斯曼尼亚人舒伯特品种的开放斑块的公式。这为Kummini-Lakshmibai-Sastry-Seshadri（2015）的猜想提供了更正。
We give degree formulas for Grothendieck polynomials indexed by vexillary permutations and $1432$-avoiding permutations via tableau combinatorics. These formulas generalize a formula for degrees of symmetric Grothendieck polynomials which appeared in previous joint work of the authors with Y. Ren and A. St. Dizier. We apply our formulas to compute Castelnuovo-Mumford regularity of classes of generalized determinantal ideals. In particular, we give combinatorial formulas for the regularities of all one-sided mixed ladder determinantal ideals. We also derive formulas for the regularities of certain Kazhdan-Lusztig ideals, including those coming from open patches of Schubert varieties in Grassmannians. This provides a correction to a conjecture of Kummini-Lakshmibai-Sastry-Seshadri (2015).
