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.

Spis treści:
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. Hernández Ruipérez 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. Álvarez-Cónsul and A. King
8. Coherent Systems, a brief survey S. B. Bradlow
9. Higgs bundles surface group representations Oscar García-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. Brînzănescu
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.