GENERATING THE IDEALS DEFINING UNIONS OF SCHUBERT VARIETIES

ABSTRACT. This note computes a Gröbner basis for the ideal defining a union of Schubert varieties. More precisely, it computes a Gröbner basis for unions of schemes given by northwest rank condi-tions on the space of all matrices of a fixed size. Schemes given by northwest rank conditions include classical determinantal varieties and matrix Schubert varieties–closures of Schubert varieties lifted from the flag manifold to the space of matrices. 1