On the cohomology of rank two vector bundles on P2 and a theorem of Chiantini and Valabrega

2019/01/03 by Philippe Ellia, Ellia, Philippe
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1901.00807

openalex publication_date 2019/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a normalized rank two vector bundle, E, on P2 splits if and only if h1(E(-1)) = 0. Using this fact we give another proof of a theorem of Chiantini and Valabrega. Finally we describe the normalized bundles with h1(E(-1)) <= 4.

Citations

• Nearly free divisors and rational cuspidal curves

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