Moduli Spaces and Vector Bundles

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 García-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.

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.