Projective Varieties, Linear Systems and Vector Bundles
Author: Lawrence Ein
Publisher:
Published: 1994
Total Pages: 136
ISBN-13:
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Complex Algebraic Varieties
Author: Klaus Hulek
Publisher: Springer
Published: 2006-11-14
Total Pages: 184
ISBN-13: 3540467866
DOWNLOAD EBOOKThe Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to talks given at the conference: all are original, fully refereed research articles. CONTENTS: A. Beauville: Annulation du H(1) pour les fibres en droites plats.- M. Beltrametti, A.J. Sommese, J.A. Wisniewski: Results on varieties with many lines and their applications to adjunction theory.- G. Bohnhorst, H. Spindler: The stability of certain vector bundles on P(n) .- F. Catanese, F. Tovena: Vector bundles, linear systems and extensions of (1).- O. Debarre: Vers uns stratification de l'espace des modules des varietes abeliennes principalement polarisees.- J.P. Demailly: Singular hermitian metrics on positive line bundles.- T. Fujita: On adjoint bundles of ample vector bundles.- Y. Kawamata: Moderate degenerations of algebraic surfaces.- U. Persson: Genus two fibrations revisited.- Th. Peternell, M. Szurek, J.A. Wisniewski: Numerically effective vector bundles with small Chern classes.- C.A.M. Peters: On the rank of non-rigid period maps in the weight one and two case.- A.N. Tyurin: The geometry of the special components of moduli space of vector bundles over algebraic surfaces of general type.
Vector Bundles on Algebraic Varieties
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.
Projective Duality and Homogeneous Spaces
Author: Evgueni A. Tevelev
Publisher: Springer Science & Business Media
Published: 2006-03-30
Total Pages: 257
ISBN-13: 3540269576
DOWNLOAD EBOOKProjective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until now scattered across the literature. Thus the appearance of a book specifically devoted to projective duality is a long-awaited and welcome event. Projective Duality and Homogeneous Spaces covers a vast and diverse range of topics in the field of dual varieties, ranging from differential geometry to Mori theory and from topology to the theory of algebras. It gives a very readable and thorough account and the presentation of the material is clear and convincing. For the most part of the book the only prerequisites are basic algebra and algebraic geometry. This book will be of great interest to graduate and postgraduate students as well as professional mathematicians working in algebra, geometry and analysis.
Methods of Algebraic Geometry in Control Theory: Part II
Author: Peter Falb
Publisher: Springer Science & Business Media
Published: 1990
Total Pages: 408
ISBN-13: 9780817641139
DOWNLOAD EBOOK"Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is quite satisfactory and natural for scalar systems, the study of multi-input, multi-output linear time invariant control systems requires projective algebraic geometry. Thus, this second volume deals with multi-variable linear systems and pro jective algebraic geometry. The results are deeper and less transparent, but are also quite essential to an understanding of linear control theory. A review of * From the Preface to Part 1. viii Preface the scalar theory is included along with a brief summary of affine algebraic geometry (Appendix E).
Positivity in Algebraic Geometry I
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.
The Adjunction Theory of Complex Projective Varieties
Author: Mauro Beltrametti
Publisher: Walter de Gruyter
Published: 1995
Total Pages: 424
ISBN-13: 9783110143553
DOWNLOAD EBOOKThe aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Aix-Marseille Université, France Katrin Wendland, Trinity College Dublin, Dublin, Ireland Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
The Adjunction Theory of Complex Projective Varieties
Author: Mauro C. Beltrametti
Publisher: Walter de Gruyter
Published: 2011-06-03
Total Pages: 421
ISBN-13: 3110871742
DOWNLOAD EBOOKThe aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Ample Subvarieties of Algebraic Varieties
Author: Robin Hartshorne
Publisher: Springer
Published: 2006-11-15
Total Pages: 271
ISBN-13: 3540363459
DOWNLOAD EBOOKVector Bundles and Projective Varieties
Author: Nicholas John Marino
Publisher:
Published: 2019
Total Pages: 54
ISBN-13:
DOWNLOAD EBOOKVector bundles play a prominent role in the study of projective algebraic varieties. Vector bundles can describe facets of the intrinsic geometry of a variety, as well as its relationship to other varieties, especially projective spaces. Additionally, being among the simplest examples of coherent sheaves, they can be manipulated by a wealth of technical machinery. Here we outline the general theory of vector bundles and describe their classification and structure. We also consider some special bundles and general results in low dimensions, especially rank 2 bundles and surfaces, as well as bundles on projective spaces. Finally, we indicate some open problems and current areas of research.
