Cohomology of vector bundles and non-pluriharmonic loci

Abstract

In this paper, we study cohomology groups of vector bundles on neighborhoods of a non-pluriharmonic locus in Stein manifolds and in projective manifolds. By using our results, we show variants of the Lefschetz hyperplane theorem.

We generalize our main results. Analytic parts (Section 2, 3, 4) are unchanged