2013/10/23 by Jen-Chieh Hsiao, Hsiao, Jen-Chieh
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.1310.6473
openalex publication_date 2013/10/23 · arxiv created 2013/10/24 · arxiv updated 2013/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize complete intersection matrix Schubert varieties, generalizing the classical result on one-sided ladder determinantal varieties. We also give a new proof of the F-rationality of matrix Schubert varieties. Although it is known that such varieties are F-regular (hence F-rational) by the global F-regularity of Schubert varieties, our proof is of independent interest since it does not require the Bott-Samelson resolution. As a consequence, this provides an alternative proof of the classical fact that Schubert varieties in flag varieties are normal and have rational singularities.