Semiample vector bundles and a characterization of étale trivial vector bundles

2025/09/18 by Indranil Biswas, Biswas, Indranil, D. S. Nagaraj +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2509.14606

openalex publication_date 2025/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a vector bundle E over a smooth complex projective variety M is étale trivial if and only if E is semiample and c₁(E) ∈ H²(M, \mathbb Q) vanishes. Also, a vector bundle E over a smooth complex projective curve is semiample if and only if it is virtually globally generated.

Citations

• Semiample and k-ample vector bundles

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