Free Delivery Over $100
|
|
|||
|
||||
OverviewThis 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. Full Product DetailsAuthor: Juan C. MigliorePublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Volume: v. 165 ISBN: 9783764340278ISBN 10: 3764340274 Pages: 224 Publication Date: July 1998 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Replaced By: 9780817640279 Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPart 1 Background: finitely generated graded S-modules; the deficiency modules (Mi)(V); hyperplane and hypersurface sections; Artinian reductions and h-vectors; examples. Part 2 Submodules of the deficiency module: measuring deficiency; generalizing Dubreil's theorem; lifting the Cohen-Macaulay property. Part 3 Buchsbaum curves: liaison addition; constructing Buchsbaum curves in P3. Part 4 Gorenstein subschemes of Pn: basic results on Gorenstein ideals; constructions of Gorenstein schemes - intersection of linked schemes, sections of Buchsbaum-Rim sheaves of odd rank, linear systems on aCM scheme; codimension three Gorenstein ideals. Part 5 Liaison theory: definition and first example; relations between linked schemes; the Hartshorne-Schenzel theorem; the structure of an even liaison class; geometric invariants of a liaison class. Part 6 Liaison theory in codimension two: the aCM situation and generalizations; Rao's results; the Lazarsfeld-Rao property; applications - smooth curves in P3, smooth surfaces in P4 and threefold in P5, possible degrees and genera in a codimension two even liaison class, stick figures, low rank vector bundles and schemes defined by a small number of equations.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
||||
