Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties
Jack Chen-An Chou
Source abstract
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.
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