2018/09/19 by Sheng Rao, Song Yang, Rao, Sheng +3
Mathematics · #14D07 #18G40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Primary 32S45 #Secondary 14E05
paper · pdf · doi:10.48550/arxiv.1809.07277
openalex publication_date 2018/09/19 · openalex created_date 2018/09/27 · openalex updated_date 2026/07/28
We use a sheaf-theoretic approach to obtain a blow-up formula for Dolbeault cohomology groups with values in the holomorphic vector bundle over a compact complex manifold. As applications, we present several positive (or negative) examples associated to the vanishing theorems of Girbau, Kawamata-Viehweg and Green-Lazarsfeld in a uniform manner and study the blow-up invariance of some classical holomorphic invariants.