2015/11/24 by Mihai Halic, Halic, Mihai
Mathematics · #14B20 #14C20 #14C25 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1511.07524
openalex publication_date 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this article is twofold. On one hand, we study the subvarieties of projective varieties which possess partially ample normal bundle; we prove that they are G2 in the ambient space. This generalizes results of Hartshorne and Bădescu-Schneider. We work with the cohomological partial ampleness introduced by Totaro. On the other hand, we define the concept of a partially ample subvariety, which generalizes the notion of an ample subvariety introduced by Ottem. We prove that partially ample subvarieties enjoy the stronger G3 property. Moreover, we present an application to a connectedness problem posed by Fulton-Hansen and Hartshorne. The results are illustrated with examples.