Applications of Liaison

J. Migliore; U. Nagel

doi:10.1007/978-3-030-89694-2_17

Applications of Liaison

J. Migliore, U. Nagel

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Over the course of more than 150 years a beautiful theory of liaison has emerged. Classically, complete intersections were used for the links. A systematic study of liaison theory where one uses, more generally, arithmetically Gorenstein schemes was begun only in the last few decades. It led to a flurry of new insights and applications. After reviewing some needed concepts and results, several of these applications are discussed. Topics include Hilbert functions and free resolutions, hyperplane arrangements, Gröbner bases, Rees algebras, simplicial complexes and more.

Original language	English
Title of host publication	Commutative Algebra
Subtitle of host publication	Expository Papers Dedicated to David Eisenbud on the Occasion of his 75th Birthday
Pages	501-522
Number of pages	22
ISBN (Electronic)	9783030896942
DOIs	https://doi.org/10.1007/978-3-030-89694-2_17
State	Published - Jan 1 2022

Bibliographical note

Publisher Copyright:
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021.

Keywords

Basic double link
Ferrers ideal
Graded Betti number
Gröbner basis
Hyperplane arrangement
Liaison
Rees algebra
Simplicial polytope
Stick figure
Unprojection
Vertex decomposability

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-030-89694-2_17

Cite this

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KW - Graded Betti number

KW - Gröbner basis

KW - Hyperplane arrangement

KW - Liaison

KW - Rees algebra

KW - Simplicial polytope

KW - Stick figure

KW - Unprojection

KW - Vertex decomposability

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Applications of Liaison

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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