2006/12/01 by Ning Hao, Li Li, Hao, Ning +1 · 2 citations
Mathematics · #14F10 #32L10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0612006
openalex publication_date 2006/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we compute the dimensions of the 1st and 2nd cohomology groups of all the pluricanonical bundles for Hirzebruch surfaces, and the dimensions of the 1st and 2nd cohomology groups of the second pluricanonical bundles for a blow-up of a projective plane along finite many distinct points. Both of them give examples showing that the higher cohomology of the pluricanonical bundle is not deformation invariant.