Gröbner geometry for skew-symmetric matrix Schubert varieties

Matrix Schubert varieties are the closures of orbits B×B acting on all n×n matrices, where B is group invertible lower triangular matrices. Extending work Fulton, Knutson and Miller identified a Gröbner basis for prime ideals these varieties. They also showed that corresponding initial Stanley-Reisner shellable simplicial complexes, derived related primary decomposition in terms reduced pipe dreams. These results lead to geometric proof Billey-Jockusch-Stanley formula polynomial, among many other applications. We define skew-symmetric matrix be nonempty intersections with subspace In analogy Miller's work, we describe natural generating set then compute basis. Using results, identify involving certain fpf-involution show likewise complexes. As an application, give explicit function symplectic Grothendieck polynomials. Our methods differ from can used new proofs some their as explain at end this article.