PreprintarXiv licencearXiv
Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties
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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BibTeX
@misc{chou2026castelnuovomumford,
title = {{Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties}},
author = {Jack Chen-An Chou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24957},
eprint = {2609.24957},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24957},
}
RIS
TY - UNPB
TI - Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties
AU - Jack Chen-An Chou
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24957
UR - https://arxiv.org/abs/2609.24957
AB - 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.
ER -