A very powerful technique in commutative algebra was introduced by Macaulay, who realized that studying the initial terms of elements of an ideal gives one great insight into the algebra and… Expand

A theorem of Pappus of Alexandria, proved in the fourth century A.D., began a long development in algebraic geometry. In its changing expressions one can see reflected the changing concerns of the… Expand

Introduction 389 w Notation and conventions 392 w Deformations of cohomology groups 392 w Generic vanishing criteria for topologically trivial line bundles 397 w A Nakano-type generic vanishing… Expand

Using a modified version of a technique of R. Brody, a simple proof is found that the complement of 2n + 1 hyperplanes in general position in P, is complete hyperbolic and hyperbolically embedded in… Expand

Our purpose is to study the cohomological properties of topologically trivial holomorphic line bundles on a compact Kahler manifold. (See [GLl, GL2] for our prior work on this topic.) Let M be a… Expand