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Introduction to Liaison Theory and Deficiency Modules

- J. Migliore
- Mathematics
- 1998

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 the… Expand

269 19

Gorenstein liaison, complete intersection liaison invariants and unobstructedness

- Jan O. Kleppe, J. Migliore, R. Miró-Roig, U. Nagel, C. Peterson
- Mathematics
- 2001

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-liaison… Expand

137 9

Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers

- J. Migliore, U. Nagel
- Mathematics
- 28 March 2001

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 possible… Expand

71 6- PDF

Star configurations in Pn

- A. Geramita, B. Harbourne, J. Migliore
- Mathematics
- 15 February 2013

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 point… Expand

79 6- PDF

Lifting monomial ideals

- J. Migliore, U. Nagel
- Mathematics
- 7 July 1999

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 to… Expand

31 6- PDF

Line arrangements and configurations of points with an unexpected geometric property

- D. Cook, B. Harbourne, J. Migliore, U. Nagel
- Mathematics
- Compositio Mathematica
- 6 February 2016

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 points… Expand

44 6- PDF

A tour of the Weak and Strong Lefschetz Properties

- J. Migliore, U. Nagel
- Mathematics
- 26 September 2011

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 done… Expand

80 4- PDF

Geometric consequences of extremal behavior in a theorem of Macaulay

- Anna Maria Bigatti, A. Geramita, J. Migliore
- Mathematics
- 1994

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 graded… Expand

59 4- PDF

Determinantal schemes and Buchsbaum-Rim sheaves

- M. Kreuzer, J. Migliore, U. Nagel, C. Peterson
- Mathematics
- 26 August 1997

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

22 4- PDF

Classifying Hilbert functions of fat point subschemes in ℙ2

- A. Geramita, B. Harbourne, J. Migliore
- Mathematics
- 19 May 2009

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 this… Expand

32 3- PDF

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