A vanishing theorem

2012/11/27 by Nahm Werner, Werner, Nahm, F. Laytimi +1
Mathematics · #1991: 14F17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1211.6283

openalex publication_date 2012/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E be a vector bundle and L be a line bundle over a smooth projective variety X. In this article, we give a condition for the vanishing of Dolbeault cohomology groups of the form H^p,q(X,\SSS^αE⊗ \wedge^β E⊗ L) when S^α+βE ⊗ L is ample. This condition is shown to be invariant under the interchange of p and q. The optimality of this condition is discussed for some parameter values.

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