Moduli spaces and vector bundles
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Bibliographic Information
Moduli spaces and vector bundles
（London Mathematical Society lecture note series, 359）
Cambridge University Press, 2009
- : pbk
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Other editors: Leticia Brambila-Paz, Oscar García-Prada, S. Ramanan
Includes bibliographical references
Description and Table of Contents
Description
Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string theory. Peter E. Newstead has been a leading figure in this field almost from its inception and has made many seminal contributions to our understanding of moduli spaces of stable bundles. This volume has been assembled in tribute to Professor Newstead and his contribution to algebraic geometry. Some of the subject's leading experts cover foundational material, while the survey and research papers focus on topics at the forefront of the field. This volume is suitable for both graduate students and more experienced researchers.
Table of Contents
- Preface
- Acknowledgments
- Part I. Lecture Notes: 1. Lectures on principal bundles V. Balaji
- 2. Brill-Noether theory for stable vector bundles Ivona Grzegorczyk and Montserrat Teixidor i Bigas
- 3. Fourier-Mukai and Nahm transforms U. Bruzzo, D. Hernandez Ruiperez and C. Tejero Prieto
- 4. Geometric invariant theory P. E. Newstead
- 5. Deformation theory for vector bundles N. Nitsure
- 6. The theory of vector bundles S. Ramanan
- Part II. Survey articles: 7. Moduli of sheaves from moduli of Kronecker modules L. Alvarez-Consul and A. King
- 8. Coherent Systems: a brief survey S. B. Bradlow
- 9. Higgs bundles surface group representations Oscar Garcia-Prada
- 10. Quotients by non-reductive algebraic group actions Frances Kirwan
- 11. Dualities on T*SUx(2,Ox) E. Previato
- 12. Moduli spaces for principal bundles A. H. W. Schmitt
- Part III. Research Articles: 13. Beilinson type spectral sequences on scrolls M. Aprodu and V. Brinzanescu
- 14. Coherent systems on a nodal curve Usha N. Bhosle
- 15. Brill-Noether bundles and coherent systems on special curves L. Brambila-Paz and Angela Ortega
- 16. Higgs bundles in the vector representation N. Hitchin
- 17. Moduli spaces of torsion free sheaves on nodal curves C. S. Seshadri.
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