2023/01/02 by Syu Kato, Kato, Syu · 1 citation
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2301.00862
openalex publication_date 2023/01/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a smooth projective variety \mathscr XΨ that compactifies an equivariant vector subbundle of the cotangent bundle of the flag variety for GL(n), determined by a root ideal Ψ. A natural family of line bundles on \mathscr XΨ yields the Catalan functions -- symmetric functions introduced by Chen--Haiman and studied further by Blasiak--Morse--Pun--Summers. By analyzing the geometry of \mathscr XΨ, we prove the vanishing conjecture of Chen--Haiman, confirm the tame case of the vanishing conjecture of Blasiak--Morse--Pun, and establish the monotonicity conjectures of Shimozono--Weyman.