Vector Bundles on Complex Projective Spaces

With an Appendix by S. I. Gelfand
1980
ISBN: 978-3-0348-0150-8
Verlag: Springer

Buch, Englisch, 239 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 382 g

Reihe: Modern Birkhäuser Classics

These 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.

Zielgruppe

Research

Autoren/Hrsg.

Okonek, Christian

Spindler, Heinz

Schneider, Michael

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

Introduction.- Chapter 1. Holomorphic vector bundles and the geometry of Pn.- Chapter 2. Stability and moduli spaces.- Bibliography.- Supplemental Bibliography.- Index.- Appendix A. Sheaves on Pn and problems in linear algebra.- Bibliography for Appendix A.

Über Autor(innen)

Schneider, Michael
Michael Schneider was Professor for algebraic geometry at the University of Bayreuth, deceased in 1997.

Okonek, Christian
Christian Okonek is Professor for mathematics at the University of Zurich.

Spindler, Heinz
Heinz Spindler is Professor for mathematics at the University of Osnabrück.

Christian Okonek is Professor for mathematics at the University of Zurich. Michael Schneider was Professor for algebraic geometry at the University of Bayreuth, deceased in 1997. Heinz Spindler is Professor for mathematics at the University of Osnabrück.