Moduli Spaces and Vector Bundles
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.
- Electronic book text | 516 pages
- 12 Dec 2011
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
- 9 b/w illus.
About Leticia Brambila-Paz
Leticia Brambila-Paz is a Professor Titular in the Centro de Investigacion en Matematicas at the University of Guanajuato, Mexico. Steven B. Bradlow is a Professor in the Department of Mathematics at the University of Illinois at Urbana-Champaign. Oscar Garcia-Prada is a Research Professor in the Instituto de Ciencias Matematicas at Consejo Superior de Investigaciones Cientificas. S. Ramanan is a Retired Distinguished Professor from the Tata Institute of Fundamental Research in Mumbai. He is currently an Adjunct Professor at the Chennai Mathematical Institute in India.
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.