Introduction to Liaison Theory and Deficiency Modules PDF Download
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Author: Juan C. Migliore
Publisher: Springer Science & Business Media
ISBN: 1461217946
Category : Mathematics
Languages : en
Pages : 218
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Book Description
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.
Author: Juan C. Migliore
Publisher: Springer Science & Business Media
ISBN: 1461217946
Category : Mathematics
Languages : en
Pages : 218
Get Book Here
Book Description
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.
Author: Juan Carlos Migliore
Publisher:
ISBN: 9783764340278
Category : Graded modules
Languages : en
Pages : 215
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Book Description
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.
Author: Juan Carlos Migliore
Publisher:
ISBN:
Category : Geometry, Algebraic
Languages : en
Pages : 166
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Book Description
Author: Maria Emilia Alonso
Publisher: Springer Science & Business Media
ISBN: 3034602014
Category : Mathematics
Languages : en
Pages : 294
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Book Description
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.
Author: Ryoshi Hotta
Publisher: Springer Science & Business Media
ISBN: 081764363X
Category : Mathematics
Languages : en
Pages : 408
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Book Description
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.
Author: Sundaram Thangavelu
Publisher: Springer Science & Business Media
ISBN: 0817681647
Category : Mathematics
Languages : en
Pages : 189
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Book Description
In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.
Author: James Lepowsky
Publisher: Springer Science & Business Media
ISBN: 9780817634087
Category : Mathematics
Languages : en
Pages : 344
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Book Description
The deep and relatively new field of vertex operator algebras is intimately related to a variety of areas in mathematics and physics: for example, the concepts of "monstrous moonshine," infinite-dimensional Lie theory, string theory, and conformal field theory. This book introduces the reader to the fundamental theory of vertex operator algebras and its basic techniques and examples. Beginning with a detailed presentation of the theoretical foundations and proceeding to a range of applications, the text includes a number of new, original results and also highlights and brings fresh perspective to important works of many researchers. After introducing the elementary "formal calculus'' underlying the subject, the book provides an axiomatic development of vertex operator algebras and their modules, expanding on the early contributions of R. Borcherds, I. Frenkel, J. Lepowsky, A. Meurman, Y.-Z. Huang, C. Dong, Y. Zhu and others. The concept of a "representation'' of a vertex (operator) algebra is treated in detail, following and extending the work of H. Li; this approach is used to construct important families of vertex (operator) algebras and their modules. Requiring only a familiarity with basic algebra, Introduction to Vertex Operator Algebras and Their Representations will be useful for graduate students and researchers in mathematics and physics. The booka??s presentation of the core topics will equip readers to embark on many active research directions related to vertex operator algebras, group theory, representation theory, and string theory.
Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 9780817642594
Category : Mathematics
Languages : en
Pages : 844
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Book Description
This book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. The book initially shares insights that make use of actual matrices; it later relies on such structural features as properties of root systems.
Author: Alexander Reznikov
Publisher: Springer Science & Business Media
ISBN: 1461213142
Category : Mathematics
Languages : en
Pages : 332
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Book Description
This book is an outgrowth of the Workshop on "Regulators in Analysis, Geom etry and Number Theory" held at the Edmund Landau Center for Research in Mathematical Analysis of The Hebrew University of Jerusalem in 1996. During the preparation and the holding of the workshop we were greatly helped by the director of the Landau Center: Lior Tsafriri during the time of the planning of the conference, and Hershel Farkas during the meeting itself. Organizing and running this workshop was a true pleasure, thanks to the expert technical help provided by the Landau Center in general, and by its secretary Simcha Kojman in particular. We would like to express our hearty thanks to all of them. However, the articles assembled in the present volume do not represent the proceedings of this workshop; neither could all contributors to the book make it to the meeting, nor do the contributions herein necessarily reflect talks given in Jerusalem. In the introduction, we outline our view of the theory to which this volume intends to contribute. The crucial objective of the present volume is to bring together concepts, methods, and results from analysis, differential as well as algebraic geometry, and number theory in order to work towards a deeper and more comprehensive understanding of regulators and secondary invariants. Our thanks go to all the participants of the workshop and authors of this volume. May the readers of this book enjoy and profit from the combination of mathematical ideas here documented.
Author: Peter Bouwknegt
Publisher: Springer Science & Business Media
ISBN: 1461200679
Category : Mathematics
Languages : en
Pages : 213
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Book Description
In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.
