A Generalization of Kodaira-Ramanujam's Vanishing Theorem.

TL;DR: Theorem 1.1 as discussed by the authors deals with a sort of inequality for the first and second Chern classes of normal projective varieties with numerically effective canonical classes (1.1); to some extent it is a continuation of the author's previous paper [Mil] in which the surface case was discussed.

TL;DR: In this article, the authors consider the properties of vector bundles and show that vector bundles can be classified into three classes: vector bundles, line bundles, and vector bundles with line bundles.

TL;DR: In this paper, a singular hermitian metric on a holomorphic line bundle is introduced as a tool for the study of various algebraic questions, and the coefficients of isolated logarithmic poles of a plurisubharmonic singular metric are shown to have a simple interpretation in terms of the constant e of Seshadri's ampleness criterion.

TL;DR: In this article, the authors work over an algebraically closed field of characteristic zero, which they may assume is the field of complex numbers and adhere to the notations of the paper referred to in the title.