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Generic Initial Ideals
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 andExpand
Cayley-Bacharach theorems and conjectures
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 theExpand
Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville
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 vanishingExpand
The hyperbolicity of the complement of 2+1 hyperplanes in general position in _{} and related results
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 inExpand
Higher obstructions to deforming cohomology groups of line bundles
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 aExpand