Applications of Liaison

J. Migliore () and U. Nagel ()
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J. Migliore: University of Notre Dame, Department of Mathematics
U. Nagel: University of Kentucky, Department of Mathematics

A chapter in Commutative Algebra, 2021, pp 523-568 from Springer

Abstract: 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.

Keywords: Liaison; Basic double link; Stick figure; Hyperplane arrangement; Graded Betti number; Simplicial polytope; Gröbner basis; Ferrers ideal; Rees algebra; Vertex decomposability; Unprojection (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-89694-2_17

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

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