Vector Bundles in Algebraic Geometry

ISBN-13: 9780521498784 / Angielski / Miękka / 1995 / 356 str.

N. J. Hitchin; W. M. Oxbury; P. E. Newstead

Opis

Successive waves of migrant concepts, largely from mathematical physics, have stimulated the study of vector bundles over algebraic varieties in the past few years. But the subject has retained its roots in old questions concerning subvarieties of projective space. The 1993 Durham Symposium on vector bundles in algebraic geometry brought together some of the leading researchers in the field to further explore these interactions. This book is a collection of survey articles by the main speakers at the Symposium and presents to the mathematical world an overview of the key areas of research involving vector bundles. Topics include augmented bundles and coherent systems which link gauge theory and geometric invariant theory; Donaldson invariants of algebraic surfaces; Floer homology and quantum cohomology; conformal field theory and the moduli spaces of bundles on curves; the Horrocks-Mumford bundle and codimension 2 subvarieties in p4 and p5; and exceptional bundles and stable sheaves on projective space. This book will appeal greatly to mathematicians working in algebraic geometry and areas adjoining mathematical physics.

Spis treści

1. On the deformation theory of moduli spaces of vector bundles V. Balaji and P. Vishwanath; 2. Stable augmented bundles over Riemann surfaces S. Bradlow, G. Daskapoulos, O. Garcia-Pradia and R. Wentworth; 3. On surfaces in P4 and threefolds in P5 W. Decker and S. Popescu; 4. Exceptional bundles and moduli spaces of stable sheaves on Pn J. M. Drezet; 5. Floer homology and algebraic geometry S. Donaldson; 6. The Horrocks-Mumford bundle K. Hulek; 7. Faisaux semi-stable et systems coherent J. Le Potier; 8. Combinatorics of the Verlinde formula A. Szenes; 9. Canonical and almost canonical spin polynomials of an algebraic surface A. Tyurin; 10. On conformal field theory K. Ueno.