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…mehr
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.
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. Brînz¿nescu 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.
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. Brînz¿nescu 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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