Coherent Variety
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Coherent Variety
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Author : Micheal D. Clark
language : en
Publisher: Praeger
Release Date : 1983-01-26
Coherent Variety written by Micheal D. Clark and has been published by Praeger this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-26 with Philosophy categories.
Introduction To Singularities
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Author : Shihoko Ishii
language : en
Publisher: Springer
Release Date : 2014-11-19
Introduction To Singularities written by Shihoko Ishii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.
This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dim ensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied.
Cohomology Of Coherent Sheaves On Projective Varieties
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Author : Rahul Pandharipande
language : en
Publisher:
Release Date : 1990
Cohomology Of Coherent Sheaves On Projective Varieties written by Rahul Pandharipande and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Hodge Theory Mn 49
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Author : Eduardo Cattani
language : en
Publisher: Princeton University Press
Release Date : 2014-07-21
Hodge Theory Mn 49 written by Eduardo Cattani and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-21 with Mathematics categories.
This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kähler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck’s algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne’s theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.
Coherent Sheaves On Varieties Arising In Springer Theory And Category 0
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Author : Vinoth Nandakumar
language : en
Publisher:
Release Date : 2015
Coherent Sheaves On Varieties Arising In Springer Theory And Category 0 written by Vinoth Nandakumar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
In this thesis, we will study three topics related to Springer theory (specifically, the geometry of the exotic nilpotent cone, and two-block Springer fibers), and stability conditions for category 0. In the first chapter, we will be studying the geometry of the exotic nilpotent cone (which is a variant of the nilpotent cone in type C introduced by Kato). Bezrukavnikov has established a bijection between A+, the dominant weights for an arbitrary simple algebraic group H, and 0, the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit (as originally conjectured by Lusztig and Vogan). Here we prove an analogous statement for the exotic nilpotent cone. In the second chapter (which is based on joint work with Rina Anno), we study the exotic t-structure for a two-block Springer fibre (i.e. for a nilpotent matrix of type (m + n, n) in type A). The exotic t-structure has been defined by Bezrukavnikov and Mirkovic for Springer theoretic varieties in order to study representations of Lie algebras in positive characteristic. Using techniques developed by Cautis and Kamnitzer, we show that the irreducible objects in the heart of the exotic t-structure are indexed by crossingless (m, m + 2n) matchings. We also show that the resulting Ext algebras resemble Khovanov's arc algebras (but placed on an annulus). In the third chapter, we study stability conditions on certain sub-quotients of category 0. Recently, Anno, Bezrukavnikov and Mirkovic have introduced the notion of a "real variation of stability conditions" (which are related to Bridgeland's stability conditions), and construct an example using categories of coherent sheaves on Springer fibers. Here we construct another example, by studying certain sub-quotients of category 0 with a fixed Gelfand-Kirillov dimension. We use the braid group action on the derived category of category 0, and certain leading coefficient polynomials coming from translation functors.
Semi Infinite Algebraic Geometry Of Quasi Coherent Sheaves On Ind Schemes
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Author : Leonid Positselski
language : en
Publisher: Springer Nature
Release Date : 2023-10-16
Semi Infinite Algebraic Geometry Of Quasi Coherent Sheaves On Ind Schemes written by Leonid Positselski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-16 with Mathematics categories.
Semi-Infinite Geometry is a theory of "doubly infinite-dimensional" geometric or topological objects. In this book the author explains what should be meant by an algebraic variety of semi-infinite nature. Then he applies the framework of semiderived categories, suggested in his previous monograph titled Homological Algebra of Semimodules and Semicontramodules, (Birkhäuser, 2010), to the study of semi-infinite algebraic varieties. Quasi-coherent torsion sheaves and flat pro-quasi-coherent pro-sheaves on ind-schemes are discussed at length in this book, making it suitable for use as an introduction to the theory of quasi-coherent sheaves on ind-schemes. The main output of the homological theory developed in this monograph is the functor of semitensor product on the semiderived category of quasi-coherent torsion sheaves, endowing the semiderived category with the structure of a tensor triangulated category. The author offers two equivalent constructions of the semitensor product, as well as its particular case, the cotensor product, and shows that they enjoy good invariance properties. Several geometric examples are discussed in detail in the book, including the cotangent bundle to an infinite-dimensional projective space, the universal fibration of quadratic cones, and the important popular example of the loop group of an affine algebraic group.
Coherent Multidimensional Spectroscopy
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Author : Minhaeng Cho
language : en
Publisher: Springer
Release Date : 2019-08-06
Coherent Multidimensional Spectroscopy written by Minhaeng Cho and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-06 with Science categories.
This book will fulfill the needs of time-domain spectroscopists who wish to deepen their understanding of both the theoretical and experimental features of this cutting-edge spectroscopy technique. Coherent Multidimensional Spectroscopy (CMDS) is a state-of-the-art technique with applications in a variety of subjects like chemistry, molecular physics, biochemistry, biophysics, and material science. Due to dramatic advancements of ultrafast laser technologies, diverse multidimensional spectroscopic methods utilizing combinations of THz, IR, visible, UV, and X-ray radiation sources have been developed and used to study real time dynamics of small molecules in solutions, proteins and nucleic acids in condensed phases and membranes, single and multiple excitons in functional materials like semiconductors, quantum dots, and solar cells, photo-excited states in light-harvesting complexes, ions in battery electrolytes, electronic and conformational changes in charge or proton transfer systems, and excess electrons and protons in water and biological systems.
Coherent States Applications In Physics And Mathematical Physics
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Author : John R Klauder
language : en
Publisher: World Scientific
Release Date : 1985-04-01
Coherent States Applications In Physics And Mathematical Physics written by John R Klauder and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-04-01 with Science categories.
This volume is a review on coherent states and some of their applications. The usefulness of the concept of coherent states is illustrated by considering specific examples from the fields of physics and mathematical physics. Particular emphasis is given to a general historical introduction, general continuous representations, generalized coherent states, classical and quantum correspondence, path integrals and canonical formalism. Applications are considered in quantum mechanics, optics, quantum chemistry, atomic physics, statistical physics, nuclear physics, particle physics and cosmology. A selection of original papers is reprinted.
Coherent Control In Atoms Molecules And Semiconductors
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Author : Walter Pötz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Coherent Control In Atoms Molecules And Semiconductors written by Walter Pötz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The International Workshop on Coherent Control of Carrier Dynamics in Semiconductors was held May 19 to 22, 1998 at the University of Illinois at Chicago. Its intent was to bring together an international and interdisciplinary group of scientists to discuss recent progress, pertinent problems, and open questions in the field of coherent control in atoms, molecules, and semiconductors, in particular. Twenty-seven scientists from the physical chemistry, quantum optics, semiconductor, electrical engineering, and laser communities accepted our invitation and made this event a meeting of exciting presentations and vivid discussions. This volume contains the proceedings of this workshop. Most speakers accepted our invitation to provide a manuscript either on specific aspects of their work or a brief review of their area of research. All manuscripts were reviewed. It is hoped that they provide not merely an overview of most of the issues covered during the workshop, but also represent an account of the current state of coherent control in general. Hence, it is hoped that they are also of interest to a large number of scientists active in one of the areas listed above. The organizers of this workshop would like to thank all the participants for making this meeting a complete success. We are particularly indebted to Dr. Larry R. Cooper at the U.S. Office of Naval Research and Dr.
Discussiones Mathematicae
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Author :
language : en
Publisher:
Release Date : 1996
Discussiones Mathematicae written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Algebra categories.