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- W1612387612 abstract "In this paper we study holomorphic rank two vector bundles on the blow up of $ {bf C}^2$ at the origin. A classical theorem of Birchoff and Grothendieck says that any holomorphic vector bundle on the projective plane ${bf P}^1$ splits into a sum of line bundles. If $E$ is a holomorphic vector bundle over the blow up of $ {bf C}^2$ at the origin, then the restriction of $E$ to the exceptional divisor is a vector bundle over ${bf P}^1$ and therefore splits. Moreover we assume that $E$ is a rank two bundle that has zero first Chern class. Hence its restriction to the exceptional divisor is of the form $ {cal O}(j) oplus {cal O}(-j) $ for some integer $j.$ We denote by ${cal M}_j$ the moduli space of equivalence classes (under holomorphic isomorphisms) of rank two holomorphic vector bundles on the blow up of $ {bf C}^2$ at the origin whose restriction to the exceptional divisor is $ {cal O}(j) oplus {cal O}(-j) .$" @default.
- W1612387612 created "2016-06-24" @default.
- W1612387612 creator A5087812741 @default.
- W1612387612 date "1996-01-12" @default.
- W1612387612 modified "2023-09-27" @default.
- W1612387612 title "Holomorphic Rank Two Vector Bundles on Blow-ups" @default.
- W1612387612 hasPublicationYear "1996" @default.
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