Applications of Liaison

J. Migliore, U. Nagel

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 languageEnglish
Title of host publicationCommutative Algebra
Subtitle of host publicationExpository Papers Dedicated to David Eisenbud on the Occasion of his 75th Birthday
Number of pages22
ISBN (Electronic)9783030896942
StatePublished - 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.


  • 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


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