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On Framed Instanton Bundles and Their Deformations
Author(s) -
Matuschke Andreas
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/(sici)1522-2616(200003)211:1<109::aid-mana109>3.0.co;2-a
Subject(s) - vector bundle , mathematics , moduli space , instanton , twistor theory , isomorphism (crystallography) , pure mathematics , splitting principle , tautological line bundle , twistor space , principal bundle , space (punctuation) , codimension , frame bundle , normal bundle , mathematical analysis , geometry , mathematical physics , crystallography , crystal structure , linguistics , chemistry , philosophy
We consider a compact twistor space P and assume that there is a surface S ⊂ P , which has degree one on twistor fibres and contains a twistor fibre F , e.g. P a LeBrun twistor space ([20], [18]). Similar to [6] and [5] we examine the restriction of an instanton bundle V equipped with a fixed trivialization along F to a framed vector bundle over ( S , F ). First we develope inspired by [13] a suitable deformation theory for vector bundles over an analytic space framed by a vector bundle over a subspace of arbitrary codimension. In the second section we describe the restriction as a smooth natural transformation into a fine moduli space. By considering framed U ( r )‐instanton bundles as a real structure on framed instanton bundles over P , we show that the bijection between isomorphism classes of framed U ( r )‐instanton bundles and isomorphism classes of framed vector bundles over ( S , F ) due to [5] is actually an isomorphism of moduli spaces.