On k-ampleness equivalence

2024/02/12 by Laytimi Fatima Nahm Werner, Werner, Laytimi Fatima Nahm
Decision Sciences · Mathematics · #14F17 #Algebraic Geometry (math.AG) #FOS: Mathematics #Fuzzy Systems and Optimization #Fuzzy and Soft Set Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2402.08066

openalex publication_date 2024/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a partition a and a vector bundle E on a projective variety X let Fl_s(E) be the corresponding flag manifold. There is a line bundle \it Q_a^s on Fl_s(E) with p:Fl_s(E)→ X and \it p_*Q_a^s = S_aE. We prove, if S_aE is k-ample (in the sense of Sommese) then \it Q_a^s is k-ample. For the inverse if \it Q_a^s is k-ample, we prove that one of two the conditions of k-ampleness namely the cohomological vanishing is proved here but not yet the condition of semiamplenes of S_aE .

Related

• Ampleness equivalence and dominance for vector bundles
• Line bundles with partially vanishing cohomology
• Generation by sections and k-ampleness
• K-theory of line bundles and smooth varieties
• Parabolic k-ample bundles