Successive waves of migrant suggestions, mostly from mathematical physics, have prompted the research of vector bundles over algebraic forms long ago few years. however the topic has retained its roots in outdated questions bearing on subvarieties of projective house. The 1993 Durham Symposium on vector bundles in algebraic geometry introduced jointly many of the prime researchers within the box to additional discover those interactions. This publication is a set of survey articles by way of the most audio system on the Symposium and offers to the mathematical global an outline of the most important parts of analysis regarding vector bundles. issues contain augmented bundles and coherent structures which hyperlink gauge concept and geometric invariant idea; Donaldson invariants of algebraic surfaces; Floer homology and quantum cohomology; conformal box conception and the moduli areas of bundles on curves; the Horrocks-Mumford package and codimension 2 subvarieties in p4 and p5; and extraordinary bundles and solid sheaves on projective area. This booklet will attraction tremendously to mathematicians operating in algebraic geometry and parts adjacent mathematical physics.
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