Introduction to Liaison Theory and Deficiency Modules: 165 - Rilegato

Migliore, Juan C.

Rilegato

ISBN 10: 0817640274 ISBN 13: 9780817640279

Casa editrice: Springer Basel AG, 1998

Riassunto

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.

Su questo libro

Recensione

"Suitable for a graduate course in algebraic geometry...numerous discussions about the historical development, and...an ample and useful list of references to important original sources... Relations between linked schemes...are explained in great detail, with complete proofs and numerous examples. ...The book ends with a section which gives a flavour of some of the ways in which liaison theory has been applied in the literature. Many more applications and examples are spread throughout the text. They contribute to a lively and inspiring style. This book is a worthwhile addition to every algebraic geometer's library."

--Mathematical Reviews

"A highly specialized monograph that provides a very good introduction to contemporary research in the fields of liaison theory and deficiency modules... The author pays great attention to motivation and the geometric aspects of the theory. There are many examples through which the reader is introduced into the theory, thereby stimulating research in the field... Useful both for specialists and for postgraduate students."

--EMS Newsletter

Contenuti

1 Background.- 1.1 Finitely Generated Graded S-Modules.- 1.2 The Deficiency Modules (Mi)(V).- 1.3 Hyperplane and Hypersurface Sections.- 1.4 Artinian Reductions and h-Vectors.- 1.5 Examples.- 2 Submodules of the Deficiency Module.- 2.1 Measuring Deficiency.- 2.2 Generalizing Dubreil’s Theorem.- 2.3 Lifting the Cohen-Macaulay Property.- 3 Buchsbaum Curves and Liaison Addition.- 3.1 Buchsbaum Curves.- 3.2 Liaison Addition.- 3.3 Constructing Buchsbaum Curves in P3.- 4 Gorenstein Subschemes of Projective Space.- 4.1 Basic Results on Gorenstein Ideals.- 4.2 Constructions of Gorenstein Schemes.- 4.2.1 Intersection of Linked Schemes.- 4.2.2 Sections of Buchsbaum-Rim Sheaves of Odd Rank.- 4.2.3 Linear Systems on aCM Schemes.- 4.3 Codimension Three Gorenstein Ideals.- 5 Liaison Theory in Arbitrary Codimension.- 5.1 Definitions and First Examples.- 5.2 Relations Between Linked Schemes.- 5.3 The Hartshorne-Schenzel Theorem.- 5.4 The Structure of an Even Liaison Class.- 5.5 Geometric Invariants of a Liaison Class.- 6 Liaison Theory in Codimension Two.- 6.1 The aCM Situation and Generalizations.- 6.2 Rao’s Results.- 6.3 The Lazarsfeld-Rao Property.- 6.4 Applications.- 6.4.1 Smooth Curves in P3.- 6.4.2 Smooth Surfaces in IP4 and Threefolds in P5.- 6.4.3 Possible Degrees and Genera in a Codimension Two Even Liaison Class.- 6.4.4 Stick Figures.- 6.4.5 Low Rank Vector Bundles and Schemes Defined by a Small Number of Equations.

Dettagli dell'edizione

• Editore: Springer Basel AG
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0817640274
• ISBN 13: 9780817640279
• Rilegatura: Copertina rigida
• Numero edizione: 2
• Numero di pagine: 236
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania