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On the Connectedness of the Real Part of Moduli Spaces of Vector Bundles on Real Algebraic Surfaces

Part of: Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  09 April 2009

Edoardo Ballico
Edoardo Ballico
Affiliation:
Department of Mathematics University of Trento38050 Povo (TN)Italy e-mail: ballico@science.unitn.it
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Abstract

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Let X be a smooth projective surface with q(X) = 0 defined over R and M(X;r;c1;c2;H) the moduli space of H-stable rank r vector bundles on X with Chern classes c1 and c2. Assume either r = 3 and X(R) connected or r = 3 and X(R) =ø or r=2 and X(R) = ø. We prove that quite often M is connected.

MSC classification

Secondary: 14P99: None of the above, but in this section 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 1 , February 2000 , pp. 41 - 54
Copyright
Copyright © Australian Mathematical Society 2000

References

[B1]Ballico, E., ‘On moduli of vector bundles on rational surfaces’, Arch. Math. 49 (1987), 267–272.CrossRefGoogle Scholar
[B2]Ballico, E., ‘Real moduli of complex objects: surfaces and bundles’, Monatsh. Math. 115 (1993), 13–26.CrossRefGoogle Scholar
[BB]Ballico, E. and Brussee, R., ‘On the unbalance of vector bundles on a blown-up surface’, Technical Report, 1990.CrossRefGoogle Scholar
[BPS]Banica, C., Putinar, M. and Schumacher, G., ‘Variation der globalen Ext in Deformationen komplexer Räume’, Math. Ann. 250 (1980), 135–155.CrossRefGoogle Scholar
[BR]Benedetti, R. and Risler, J.-J., Real algebraic and semi-algebraic sets (Hermann, Paris, 1990).Google Scholar
[Bru]Brun, J., ‘Les fibrés de rank deux sur P 2 et leurs sections’, Bull. Soc. Math. France 107 (1979), 457–473.Google Scholar
[C]Catanese, F., ‘Footnotes to a theorem of I. Reider’, in: Algebraic geometry, Proceedings, L'Aquila, 1988, Lecture Notes in Math. 1417 (Springer, Berlin, 1990) pp. 67–74.Google Scholar
[GL]Gieseker, D. and Li, J., ‘Irreducibility of moduli of rank two vector bundles on algebraic surfaces’, J. Diff. Geometry 40 (1994), 23–104.Google Scholar
[GH]Griffiths, P. and Harris, J., Principles of algebraic geometry (Wiley, New York, 1978).Google Scholar
[H]Hamm, H., ‘Lokale topologische Eigenschaft komplexer Räume’, Math. Ann. 191 (1971), 235–252.CrossRefGoogle Scholar
[Ha]Hartshorne, R., Algebraic geometry (Springer, Berlin, 1977).CrossRefGoogle Scholar
[K]Kleiman, S., ‘The transversality of a general translate’, Compositio Math. 28 (1974), 287–297.Google Scholar
[L]Langton, S., ‘Valuative criteria for families of vector bundles on algebraic varieties’, Ann. of Math. 101 (1975), 88–110.CrossRefGoogle Scholar
[Li]Li, J., ‘Kodaira dimension of moduli space of vector bundles on surfaces’, Invent. Math. 115 (1993), 1–40.CrossRefGoogle Scholar
[Q]Qin, Z., ‘Moduli spaces of stable rank-2 bundles on ruled surfaces’, Invent. Math. 110 (1992), 615–625.CrossRefGoogle Scholar
[Si]Silhol, R., Real algebraic surfaces, Lecture Notes in Math. 1137 (Springer, Berlin, 1985).Google Scholar
[T]Tyurin, A. N., ‘Cycles, curves and vector bundles on an algebraic surface’, Duke Math. J. 54 (1987), 1–26.CrossRefGoogle Scholar