Positivity of vector bundles and Dominance

arXiv (Cornell University) 2026 Preprint Open access

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Authors: F. Laytimi, Werner Nahm
DOI: 10.48550/arxiv.2603.02037
Cited by: 0

Abstract

Let $E$ be a vector bundle and $S_a$, $S_b$ the Schur functors associated to partitions $a$ and $b$. Previously we have shown that ampleness of $S_aE$ implies ampleness of $S_bE$ when $a$ is greater than $b$ in the dominance partial order. Here we prove that this result generalizes to $k$-ample, semiample and nef vector bundles. Our proof uses the common algebraic nature of these three properties and an investigation of the Littlewood-Richardson rules.

Fields of Study & Subjects

Algebraic Geometry and Number Theory Advanced Combinatorial Mathematics Advanced Algebra and Geometry

Publication details

Journal / source
arXiv (Cornell University)
Publication date
2 March 2026
Language
EN
Document type
Preprint