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.
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