Introduction to Liaison Theory and Deficiency ModulesSpringer Science & Business Media, 25 ago 1998 - 218 pagine In the fall of 1992 I was invited by Professor Changho Keem to visit Seoul National University and give a series of talks. I was asked to write a monograph based on my talks, and the result was published by the Global Analysis Research Center of that University in 1994. The monograph treated deficiency modules and liaison theory for complete intersections. Over the next several years I continually thought of improvements and additions that I would like to make to the manuscript, and at the same time my research led me in directions that gave me a fresh perspective on much of the material, especially in the direction of liaison theory. This re sulted in a dramatic change in the focus of this manuscript, from complete intersections to Gorenstein ideals, and a substantial amount of additions and revisions. It is my hope that this book now serves not only as an introduction to a beautiful subject, but also gives the reader a glimpse at very recent developments and an idea of the direction in which liaison theory is going, at least from my perspective. One theme which I have tried to stress is the tremendous amount of geometry which lies at the heart of the subject, and the beautiful interplay between algebra and geometry. Whenever possible I have given remarks and examples to illustrate this interplay, and I have tried to phrase the results in as geometric a way as possible. |
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Introduction to Liaison Theory and Deficiency Modules Juan C. Migliore Anteprima non disponibile - 2012 |
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aCM curves aCM subscheme Algebra arithmetic genus arithmetically Buchsbaum arithmetically Cohen-Macaulay associated prime assume basic double links Buchsbaum curve C₁ Chapter codimension two subschemes cohomology complete intersection component Corollary curves in P3 d₁ deficiency module defined dimension divisor equidimensional Example F₁ F₂ fact finite length G₁ geometric gives graded Betti numbers graded S-module h-vector Hence Hilbert function homogeneous ideal homogeneous polynomial hyperplane section hypersurface hypersurface section ideal quotient irreducible Iv₁ Iv₂ Lazarsfeld-Rao Property Lemma Liaison Addition liaison class liaison theory linear form linearly equivalent Linkage locally Cohen-Macaulay locally free resolution Macaulay mapping cone Math matrix minimal element minimal free resolution Ov₂ projective space proof Proposition regular sequence Remark result S/Iv saturated ideal sheaf sheaves short exact sequence skew lines smooth stick figure submodules subscheme of Pn subschemes of projective Theorem union V₁ V₁ and V₂ vector bundles zeroscheme