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Introduction to Liaison Theory and Deficiency Modules
Part 1 Background: finitely generated graded S-modules the deficiency modules (Mi)(V) hyperplane and hypersurface sections Artinian reductions and h-vectors examples. Part 2 Submodules of theExpand
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Gorenstein liaison, complete intersection liaison invariants and unobstructedness
Introduction Preliminaries Gaeta's theorem Divisors on an ACM subscheme of projective spaces Gorenstein ideals and Gorenstein liaison CI-liaison invariants Geometric applications of the CI-liaisonExpand
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Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers
Abstract An SI-sequence is a finite sequence of positive integers which is symmetric, unimodal and satisfies a certain growth condition. These are known to correspond precisely to the possibleExpand
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Star configurations in Pn
Abstract Star configurations are certain unions of linear subspaces of projective space. They have appeared in several different contexts: the study of extremal Hilbert functions for fat pointExpand
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Lifting monomial ideals
We show how to lift any monomial ideal J in n variables to a saturated ideal J of the same codimension in n -+ t variables. We show that I has the same graded Betti numbers as J and we show how toExpand
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Line arrangements and configurations of points with an unexpected geometric property
We propose here a generalization of the problem addressed by the SHGH conjecture. The SHGH conjecture posits a solution to the question of how many conditions a general union $X$ of fat pointsExpand
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A tour of the Weak and Strong Lefschetz Properties
An artinian graded algebra, $A$, is said to have the Weak Lefschetz property (WLP) if multiplication by a general linear form has maximal rank in every degree. A vast quantity of work has been doneExpand
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Geometric consequences of extremal behavior in a theorem of Macaulay
F. S. Macaulay gave necessary and sufficient conditions on the growth of a nonnegative integer-valued function which determine when such a function can be the Hilbert function of a standard gradedExpand
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Determinantal schemes and Buchsbaum-Rim sheaves
Let φ be a generically surjective morphism between direct sums of line bundles on Pn and assume that the degeneracy locus, X, of φ has the expected codimension. We call Bφ=kerφ a (first)Expand
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Classifying Hilbert functions of fat point subschemes in ℙ2
The paper [10] raised the question of what the possible Hilbert functions are for fat point subschemes of the form 2p1+...+2pr, for all possible choices ofr distinct points in ℙ2. We study thisExpand
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