Download or read book Vector Bundles and Their Applications written by Glenys Luke and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the basic notions of vector bundles and their applications. The focus of attention is towards explaining the most important notions and geometric constructions connected with the theory of vector bundles. Theorems are not always formulated in maximal generality but rather in such a way that the geometric nature of the objects comes to the fore. Whenever possible examples are given to illustrate the role of vector bundles. Audience: With numerous illustrations and applications to various problems in mathematics and the sciences, the book will be of interest to a range of graduate students from pure and applied mathematics.
Download or read book Algebraic Surfaces and Holomorphic Vector Bundles written by Robert Friedman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, before the geometry of vector bundles over such surfaces is analysed. Many of the results on vector bundles appear for the first time in book form, backed by many examples, both of surfaces and vector bundles, and over 100 exercises forming an integral part of the text. Aimed at graduates with a thorough first-year course in algebraic geometry, as well as more advanced students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology, many of the results on vector bundles will also be of interest to physicists studying string theory.
Download or read book Moduli Spaces and Vector Bundles written by Steve Bradlow and published by Cambridge University Press. This book was released on 2009-05-21 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coverage includes foundational material as well as current research, authored by top specialists within their fields.
Download or read book Geometric Invariant Theory Holomorphic Vector Bundles and the Harder Narasimhan Filtration written by Alfonso Zamora Saiz and published by Springer Nature. This book was released on 2021-03-24 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.
Download or read book Vector Bundles in Algebraic Geometry written by N. J. Hitchin and published by Cambridge University Press. This book was released on 1995-03-16 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of survey articles by the main speakers at the 1993 Durham symposium on vector bundles in algebraic geometry.
Download or read book Cohomology of Vector Bundles and Syzygies written by Jerzy Weyman and published by Cambridge University Press. This book was released on 2003-06-09 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.
Download or read book Characteristic Classes written by John Willard Milnor and published by Princeton University Press. This book was released on 1974 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
Download or read book Vector Bundles written by Andrej N. Tjurin and published by Universitätsverlag Göttingen. This book was released on 2008 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a three volume collection of Andrey Nikolaevich Tyurin's Selected Works. It includes his most interesting articles in the field of classical algebraic geometry, written during his whole career from the 1960s. Most of these papers treat different problems of the theory of vector bundles on curves and higher dimensional algebraic varieties, a theory which is central to algebraic geometry and most of its applications.
Download or read book Vector Bundles and Representation Theory written by Steven Dale Cutkosky and published by American Mathematical Soc.. This book was released on 2003 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 13 papers from the conference on ``Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory''. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S1$ fixed points in Quot-schemes and mirror principle computations for Grassmanians by S.-T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.
Download or read book Differential Geometry of Complex Vector Bundles written by Shoshichi Kobayashi and published by Princeton University Press. This book was released on 2014-07-14 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Helices and Vector Bundles written by A. N. Rudakov and published by Cambridge University Press. This book was released on 1990-07-12 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arising out of a series of seminars organized in Moscow by A.N. Rudakov, this volume is devoted to the use of helices as a method for studying exceptional vector bundles, an important and natural concept in algebraic geometry.
Download or read book Positivity in Algebraic Geometry I written by R.K. Lazarsfeld and published by Springer Science & Business Media. This book was released on 2004-08-24 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.
Download or read book Moduli of Vector Bundles written by Masaki Maruyama and published by CRC Press. This book was released on 2023-05-31 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Contains papers presented at the 35th Taniguchi International Symposium held recently in Sanda and Kyoto, Japan. Details the latest developments concerning moduli spaces of vector bundles or instantons and their application. Covers a broad array of topics in both differential and algebraic geometry."
Download or read book Covariant Schr dinger Semigroups on Riemannian Manifolds written by Batu Güneysu and published by Birkhäuser. This book was released on 2017-12-22 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities. The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials. The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also includes unpublished findings and new proofs of recently published results, it will also be interesting for researchers from geometric analysis, stochastic analysis, spectral theory, and mathematical physics..
Download or read book Vector Bundles on Complex Projective Spaces written by Christian Okonek and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are intended as an introduction to the methods of classification of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = Fn. According to Serre (GAGA) the classification of holomorphic vector bundles is equivalent to the classification of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some funda mental results from these fields are summarized at the beginning. One of the authors gave a survey in the Seminaire Bourbaki 1978 on the current state of the classification of holomorphic vector bundles overFn. This lecture then served as the basis for a course of lectures in Gottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the introductory nature of this book we have had to leave out some difficult topics such as the restriction theorem of Barth. As compensation we have appended to each sec tion a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of paragraphs. Each section is preceeded by a short description of iv its contents.
Download or read book Theta Invariants of Euclidean Lattices and Infinite Dimensional Hermitian Vector Bundles over Arithmetic Curves written by Jean-Benoît Bost and published by Springer Nature. This book was released on 2020-08-21 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most up-to-date and sophisticated account of the theory of Euclidean lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves. It contains a complete description of the theta invariants which give rise to a closer parallel with the geometric case. The author then unfolds his theory of infinite Hermitian vector bundles over arithmetic curves and their theta invariants, which provides a conceptual framework to deal with the sequences of lattices occurring in many diophantine constructions. The book contains many interesting original insights and ties to other theories. It is written with extreme care, with a clear and pleasant style, and never sacrifices accessibility to sophistication.
Download or read book Differential Geometric Structures written by Walter A. Poor and published by Courier Corporation. This book was released on 2015-04-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
