Introduction to Liaison Theory and Deficiency Modules

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This work carefully examines liaison theory and deficiency modules from basic principles, taking a geometric approach. The focus is on the role of deficiency modules in algebraic geometry, particularly with respect to liaison theory, which is treated here as a subject in itself and as a tool. The structure and classification of liaison classes are explored, and a variety of ways are described in which liaison has been applied to geometric questions. The classical study of liaison via complete intersections is compared and contrasted with the relatively new study of the subject via arithmetic Gorenstein ideals.