Analytic Moduli Spaces of Simple (Co)Framed Sheaves

Hubert Flenner () and Martin Lübke ()
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Hubert Flenner: Fakultät für Mathematik der Ruhr-Universität
Martin Lübke: Leiden University, Mathematical Institute

A chapter in Complex Geometry, 2002, pp 99-109 from Springer

Abstract: Abstract Let X be a complex space and F a coherent O x -module, A F-(co)framed sheaf on X is a pair (ε, ϕ) with a coherent O x -module ε and a morphism of coherent sheaves ϕ: F F ε (resp. ϕ: ε → F). Two such pairs (ε, ϕ) and (ε′,ϕ′) are said to be isomorphic if there exists an isomorphism of sheaves α: ε →ε′ with α° ϕ = ϕ′ (resp. ϕ′° α = ϕ). A pair (α, ϕ) is called simple if its only automorphism is the identity on ε. In this note we prove a representability theorem in a relative framework, which implies in particular that there is a moduli space of simple F- (co) framed sheaves on a given compact complex space X.

Keywords: 2000; Mathematics Subject Classification; 32G13; 14D20 (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-3-642-56202-0_7

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