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.
This paper was prepared during a visit of the second author to the University of Bochum which was financed by EAGER — European Algebraic Geometry Research Training Network, contract No. HPRN-CT-2000-00099 (BBW 99.0030).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bingener, J., Darstellbarkeitskriterien für analytische Funktoren, Ann. Sci. École Norm. Sup. 13(4) (1980), 317–347.
Bingener, J., Lokale Modulräume in der analytischen Geometrie I, II, with the cooperation of S. Kosarew, Aspects of Mathematics D2, D3 (1987), Friedr. Vieweg & Sohn, Braunschweig.
Fischer, G., Complex analytic geometry. Lecture Notes in Math. 538 (1976), Springer-Verlag, Berlin-New York.
Flenner, H., Ein Kriterium für die Offenheit der Versalität, Math. Z. 178 (1981), 449–473.
Flenner, H., Eine Bemerkung über relative Ext-Garben, Math. Ann. 258 (1981), 175–182.
Flenner, H., Sundararaman, D., Analytic geometry on complex superspaces. Trans. AMS 330 (1992), 1–40.
Grothendieck, A., Dieudonné, J., Éléments de géométrie algébrique, Publ. Math. IHES 4, 8, 11, 17, 20, 24, 28, 32 (1961-1967).
Huybrechts, D., Lehn, M., Framed modules and their moduli, Internat. J. Math. 6 (1995), 297–324.
Huybrechts, D., Lehn, M., The geometry of moduli spaces of sheaves. A spects of Mathematics E31 (1997), Friedr. Vieweg & Sohn, Braunschweig.
Kosarew, S., Okonek, C., Global moduli spaces and simple holomorphic bundles, Publ. Res. Inst. Math. Sci. 25 (1989), 1–19.
Lübke, M., Lupascu, P., Isomorphy of the gauge theoretical and the deformation theoretical moduli space of simple holomorphic pairs, in preparation.
Okonek, Ch., Teleman, A., The coupled Seiberg-Witten equations, vortices, and moduli spaces of stable pairs, Internat. J. Math. 6 (1995), 893–910.
Okonek, Ch., Teleman, A., Gauge theoretical equivariant Gromov-Witten invariants and the full Seiberg-Witten invariants of ruled surfaces, preprint, 2000
Rim, D.S., Formal deformation theory, in: Séminaire de Géométrie Algébrique, SGA 7, Lecture Notes in Mathematics 288 (1972), Springer Verlag Berlin-Heidelberg-New York.
Siu, Y.T., Trautmann, G., Deformations of coherent analytic sheaves with compact supports, Mem. Amer. Math. Soc. 29(238) (1981).
Suyama, Y., The analytic moduli space of simple framed holomorphic pairs, Kyushu J. Math. 50 (1996), 65–82.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Flenner, H., Lübke, M. (2002). Analytic Moduli Spaces of Simple (Co)Framed Sheaves. In: Bauer, I., Catanese, F., Peternell, T., Kawamata, Y., Siu, YT. (eds) Complex Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56202-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-56202-0_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62790-3
Online ISBN: 978-3-642-56202-0
eBook Packages: Springer Book Archive