Positivity of line bundles on general blow ups of Hirzebruch surfaces

2025/02/05 by Cyril J. Jacob, Jacob, Cyril J., Bivas Khan +1
Mathematics · #14C20 #14E05 #14J26 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2502.03137

openalex publication_date 2025/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate various positivity properties of line bundles on general blow ups of Hirzebruch surfaces motivated by \citeHan, where the author has studied general blow ups of ℙ². For each of the properties: ampleness, global generation, very ampleness, and k-very ampleness, we provide several sufficient numerical conditions.

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