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Author: N. J. Hitchin
Publisher: Cambridge University Press
Published: 1995-03-16
Total Pages: 359
ISBN-13: 0521498783
DOWNLOAD EBOOKThis book is a collection of survey articles by the main speakers at the 1993 Durham symposium on vector bundles in algebraic geometry.
Author: Andrej N. Tjurin
Publisher: Universitätsverlag Göttingen
Published: 2008
Total Pages: 330
ISBN-13: 3938616741
DOWNLOAD EBOOKThis 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.
Author: Michael Francis Atiyah
Publisher: Oxford University Press, USA
Published: 1987
Total Pages: 580
ISBN-13:
DOWNLOAD EBOOKA collection of the original papers presented at an international colloquium on Vector Bundles on Algebraic Varieties held at the Tata Institute of Fundamental Research in 1984. The purpose of the colloquium was to highlight recent developments in the general area of vector bundles as well asprincipal bundles on both affine and projective varieties. Projective modules and quadratic spaces over general rings were among the topics covered by the colloquium.
Author: R.K. Lazarsfeld
Publisher: Springer Science & Business Media
Published: 2004-08-24
Total Pages: 414
ISBN-13: 9783540225331
DOWNLOAD EBOOKThis 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.
Author: Robert Friedman
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 333
ISBN-13: 1461216885
DOWNLOAD EBOOKA 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.
Author: Iwona Maria Grzegorczyk
Publisher:
Published: 1990
Total Pages: 100
ISBN-13:
DOWNLOAD EBOOKAuthor: Christian Okonek
Publisher: Springer Science & Business Media
Published: 2011-06-24
Total Pages: 246
ISBN-13: 3034801513
DOWNLOAD EBOOKThese lecture notes are intended as an introduction to the methods of classi?cation of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = P . According to Serre (GAGA) the class- n cation of holomorphic vector bundles is equivalent to the classi?cation 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 fundamental results from these ?elds are summarized at the beginning. One of the authors gave a survey in the S ́eminaire Bourbaki 1978 on the current state of the classi?cation of holomorphic vector bundles over P . This lecture then served as the basis for a course of lectures n in G ̈ottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the - troductory nature of this book we have had to leave out some di?cult topics such as the restriction theorem of Barth. As compensation we have appended to each section 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 pa- graphs. Each section is preceded by a short description of its contents.
Author: Fedor Bogomolov
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 229
ISBN-13: 0821828622
DOWNLOAD EBOOKThis text covers the essential topics in the geometry of algebraic curves, such as line and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups. It demonstrates how curves can act as a natural introduction to algebraic geometry.
Author: J. Le Potier
Publisher: Cambridge University Press
Published: 1997-01-28
Total Pages: 260
ISBN-13: 9780521481823
DOWNLOAD EBOOKThis work consists of two sections on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The author also discusses the construction and elementary properties of the moduli spaces of stable bundles. In particular Le Potier constructs HilbertSHGrothendieck schemes of vector bundles, and treats Mumford's geometric invariant theory. The second part centers on the structure of the moduli space of semistable sheaves on the projective plane. The author sketches existence conditions for sheaves of given rank, and Chern class and construction ideas in the general context of projective algebraic surfaces. Professor Le Potier provides a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.
Author: Kang Zuo
Publisher: Springer
Published: 2006-11-14
Total Pages: 142
ISBN-13: 3540484248
DOWNLOAD EBOOKUsing harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.
