斜对称矩阵Schubert簇的Castelnuovo-Mumford正则度
Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties
- School of Mathematics, University of Minnesota（明尼苏达大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文通过给出辛Grothendieck多项式次数的组合公式，计算了斜对称矩阵Schubert簇的Castelnuovo-Mumford正则度，并刻画了其最高次齐次分量及最大正则度。
中文摘要 AI 辅助
斜对称矩阵Schubert簇是由矩阵Schubert簇与斜对称矩阵空间相交得到的行列式簇。它们与旗簇上辛群作用的轨道闭包密切相关，其环面等变K-类是辛Grothendieck多项式。我们通过给出辛Grothendieck多项式的次数的组合公式，计算了斜对称矩阵Schubert簇的Castelnuovo-Mumford正则度。此外，我们刻画了辛Grothendieck多项式的最高次齐次分量，并计算了斜对称矩阵Schubert簇的最大Castelnuovo-Mumford正则度。
英文摘要
Skew-symmetric matrix Schubert varieties are determinantal varieties obtained by intersecting matrix Schubert varieties with the space of skew-symmetric matrices. They are closely related to the orbit closures of the symplectic group action on the flag variety, and their torus-equivariant K-classes are the symplectic Grothendieck polynomials. We compute the Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties by giving a combinatorial formula for the degree of symplectic Grothendieck polynomials. In addition, we characterize the highest-degree homogeneous component of a symplectic Grothendieck polynomial and compute the maximal Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties.
