Multiplicity-free subvarieties of flag varieties

2002/11/02 by Michel Brion, Brion, Michel · 2 citations
Computer Science · Mathematics · #14L30 #14M05 #14M15 #14N15 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:14L30 #msc:14M05 #msc:14M15 #msc:14N15

paper · pdf · doi:10.48550/arxiv.math/0211028

LaTeX, 13 pages

arxiv created 2002/11/02 · openalex publication_date 2002/11/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a flag variety Fl over an algebraically closed field, and a subvariety V whose cycle class is a multiplicity-free sum of Schubert cycles. We show that V is arithmetically normal and Cohen-Macaulay, in the projective embedding given by any ample invertible sheaf on Fl.

Cited by

• Vanishing theorems for combinatorial geometries
• The geometry of zonotopal algebras II: Orlik--Terao algebras and Schubert varieties

Related

• Non-perverse parity sheaves on the flag variety
• Mod p sheaves on Witt flags
• Multiplicity-free products of Schubert divisors
• Large Schubert varieties
• An anticanonical perspective on G/P Schubert varieties