Some vanishing theorems for 𝑘-positive line bundles twisted by pseudo-effective line bundles

Abstract

We will first present a new proof of the famous Nadel vanishing theorem by using Demailly’s equisingular approximation theorem and Hörmander L 2 L^2 estimates. Then some vanishing theorems for k k -positive line bundles twisted by pseudo-effective line bundles will be discussed by the same methods.