Abstract

T-varieties are normal varieties equipped with an action of an algebraic torus T. When the action is effective, the complexity of a T-variety X is dim(X)−dim(T). Matrix Schubert varieties, introduced by Fulton in 1992, are T-varieties consisting of n×n matrices satisfying certain constraints on the ranks of their submatrices. In this dissertation, we focus on the complexity of certain torus-fixed affine subvarieties of matrix Schubert varieties. Concretely, given a matrix Schubert variety X_w where w∈S_n, we study the complexity of Y_w obtained by the decomposition X_w = Y_w ×C^k with k as large as possible. Building on results by Escobar–Mészáros and Donten-Bury–Escobar–Portakal, we show that for a fixed n, the complexity of Y_w with respect to this action can be any integer between 0 and (n−1)(n−3), except 1.

Committee Chair

John Shareshian

Committee Members

Laura Escobar Vega, Carl Lian; Martha Precup; Matt Kerr

Degree

Doctor of Philosophy (PhD)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

4-28-2026

Language

English (en)

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Mathematics Commons

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