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Introduction to Liaison Theory and Deficiency Modules

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 946/5 ( reviews)

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Book Synopsis Introduction to Liaison Theory and Deficiency Modules by : Juan C. Migliore

Download or read book Introduction to Liaison Theory and Deficiency Modules written by Juan C. Migliore. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Liaison Theory and Deficiency Modules

1998-01-01 Graded modules
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Release : 1998-01-01
Genre : Graded modules
Kind : eBook
Book Rating : 278/5 ( reviews)

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Book Synopsis Introduction to Liaison Theory and Deficiency Modules by : Juan Carlos Migliore

Download or read book Introduction to Liaison Theory and Deficiency Modules written by Juan Carlos Migliore. This book was released on 1998-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This book carefully examines liaison theory and deficiency modules from basic principles, taking a geometric approach to the subject. The focus is on the role of deficiency modules in algebraic geometry, particularly with respect to liaison theory, which is treated here both as a subject in itself and as a rich 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 arithmetically Gorenstein ideals. It will be ideal for a graduate student or professional mathematician who wishes to learn about these topics. On the other hand, it reaches the edge of current research, and as such it will be of interest to specialists as well.

An Introduction to Deficiency Modules and Liaison Theory for Subschemes of Projective Space

1994 Geometry, Algebraic
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Release : 1994
Genre : Geometry, Algebraic
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis An Introduction to Deficiency Modules and Liaison Theory for Subschemes of Projective Space by : Juan Carlos Migliore

Download or read book An Introduction to Deficiency Modules and Liaison Theory for Subschemes of Projective Space written by Juan Carlos Migliore. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt:

Liaison, Schottky Problem and Invariant Theory

2011-01-30 Mathematics
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Release : 2011-01-30
Genre : Mathematics
Kind : eBook
Book Rating : 014/5 ( reviews)

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Book Synopsis Liaison, Schottky Problem and Invariant Theory by : Maria Emilia Alonso

Download or read book Liaison, Schottky Problem and Invariant Theory written by Maria Emilia Alonso. This book was released on 2011-01-30. Available in PDF, EPUB and Kindle. Book excerpt: Federico Gaeta (1923–2007) was a Spanish algebraic geometer who was a student of Severi. He is considered to be one of the founders of linkage theory, on which he published several key papers. After many years abroad he came back to Spain in the 1980s. He spent his last period as a professor at Universidad Complutense de Madrid. In gratitude to him, some of his personal and mathematically close persons during this last station, all of whom bene?ted in one way or another by his ins- ration, have joined to edit this volume to keep his memory alive. We o?er in it surveys and original articles on the three main subjects of Gaeta’s interest through his mathematical life. The volume opens with a personal semblance by Ignacio Sols and a historical presentation by Ciro Ciliberto of Gaeta’s Italian period. Then it is divided into three parts, each of them devoted to a speci?c subject studied by Gaeta and coordinated by one of the editors. For each part, we had the advice of another colleague of Federico linked to that particular subject, who also contributed with a short survey. The ?rst part, coordinated by E. Arrondo with the advice of R.M.

D-Modules, Perverse Sheaves, and Representation Theory

2007-11-07 Mathematics
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Release : 2007-11-07
Genre : Mathematics
Kind : eBook
Book Rating : 63X/5 ( reviews)

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Book Synopsis D-Modules, Perverse Sheaves, and Representation Theory by : Ryoshi Hotta

Download or read book D-Modules, Perverse Sheaves, and Representation Theory written by Ryoshi Hotta. This book was released on 2007-11-07. Available in PDF, EPUB and Kindle. Book excerpt: D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.

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