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Vector bundles

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The study of vector bundles over algebraic varieties has been stimulated over the last few years by successive waves of migrant concepts, largely from mathematical physics, whilst retaining 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 explore further 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 covered include those linking gauge theory and geometric invariant theory such as augmented bundles and coherent systems; 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; exceptional bundles and stable sheaves on projective space.

Vector bundles --- Fiber spaces (Mathematics)

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Vector bundles. --- D-modules. --- Fibrés vectoriels. --- D-modules, Théorie des.

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Vector bundles. --- Fibrés vectoriels. --- K-theorie --- Fibrés vectoriels.

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The authors provide a complete classification of globally generated vector bundles with first Chern class c_1 leq 5 one the projective plane and with c_1 leq 4 on the projective n-space for n geq 3. This reproves and extends, in a systematic manner, previous results obtained for c_1 leq 2 by Sierra and Ugaglia [J. Pure Appl. Algebra 213 (2009), 2141-2146], and for c_1 = 3 by Anghel and Manolache [Math. Nachr. 286 (2013), 1407-1423] and, independently, by Sierra and Ugaglia [J. Pure Appl. Algebra 218 (2014), 174-180]. It turns out that the case c_1 = 4 is much more involved than the previous cases, especially on the projective 3-space. Among the bundles appearing in our classification one can find the Sasakura rank 3 vector bundle on the projective 4-space (conveniently twisted). The authors also propose a conjecture concerning the classification of globally generated vector bundles with c_1 leq n - 1 on the projective n-space. They verify the conjecture for n leq 5.

Vector bundles. --- Geometry, Projective. --- Projective spaces. --- Chern classes.