For each n≥4, the torus-action complexity of the reduced matrix Schubert variety Y_w takes every integer value from 0 to (n−1)(n−3) except 1, with unique maximum at w=[n,n−1,…,3,1,2].
Polyhedral divisors and algebraic torus actions
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Complexity of the Zero Set of a Matrix Schubert Ideal
For each n≥4, the torus-action complexity of the reduced matrix Schubert variety Y_w takes every integer value from 0 to (n−1)(n−3) except 1, with unique maximum at w=[n,n−1,…,3,1,2].