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Moduli spaces of vector bundles over ruled surfaces

Published online by Cambridge University Press:  22 January 2016

Marian Aprodu  and
Vasile Brînzănescu
Marian Aprodu
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. BOX 1-764, RO-70700 Bucharest, Romania, [email protected]
Vasile Brînzănescu
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. BOX 1-764, RO-70700 Bucharest, Romania, [email protected]
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Abstract

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We study moduli spaces M(c1, c2, d, r) of isomorphism classes of algebraic 2-vector bundles with fixed numerical invariants c1, c2, d, r over a ruled surface. These moduli spaces are independent of any ample line bundle on the surface. The main result gives necessary and sufficient conditions for the non-emptiness of the space M(c1, c2, d, r) and we apply this result to the moduli spaces ML(c1, c2) of stable bundles, where L is an ample line bundle on the ruled surface.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 154 , 1999 , pp. 111 - 122
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

References

[B] Brînzănescu, V., Algebraic 2-vector bundles on ruled surfaces, Ann. Univ. Ferrara-Sez VII, Sc. Mat., XXXVII (1991), 55–64.CrossRefGoogle Scholar
[B-St1] Brînzănescu, V. and Stoia, M., Topologically trivial algebraic 2-vector bundles on ruled surfaces I, Rev. Roumaine Math. Pures Appl., 29 (1984), 661–673.Google Scholar
[B-St2], Topologically trivial algebraic 2-vector bundles on ruled surfaces II, In: Lect. Notes Math., 1056, Springer (1984).Google Scholar
[Br1] Brossius, J. E., Rank-2 vector bundles on a ruled surface I, Math. Ann., 265 (1983), 155–168.CrossRefGoogle Scholar
[Br2] Brossius, J. E., Rank-2 vector bundles on a ruled surface II, Math. Ann., 266 (1984), 199–214.CrossRefGoogle Scholar
[Ha] Hartshorne, R., Algebraic Geometry, Graduate Texts in Math., 49, Springer, Berlin-Heidelberg, 1977.Google Scholar
[H-S] Hoppe, H. J. and Spindler, H., Modulräume stabiler 2-Bündel auf Regelflächen, Math. Ann., 249 (1980), 127–140.CrossRefGoogle Scholar
[K] Kleiman, S., Les théorèmes de finitude pour les Founcteurs de Picard, In: Théories des intersections et théorème de Riemann-Roch, SGA VI, Exp. XIII, Lect. Notes in Math., 225, Springer (1971), 616–666.Google Scholar
[N] Nagata, M., On self-intersection Number of a section on ruled surface, Nagoya Math. J., 37 (1970), 191–196.CrossRefGoogle Scholar
[O-S-S] Okonek, C., Schneider, M. and Spindler, H., Vector bundles on complex projective spaces, Birkhäuser, Basel Boston Stuttgart, 1980.Google Scholar
[Q1] Qin, Z., Moduli spaces of stable rank-2 bundles on ruled surfaces, Invent. Math., 110 (1992), 615–626.CrossRefGoogle Scholar
[Q2] Qin, Z., Equivalence classes of polarizations and moduli spaces of sheaves, J. Diff. Geom., 37 (1993), 397–415.Google Scholar
[Se] Serre, J. P., Sur les modules projectifs, Sém. Dubreil-Pisot 1960/1961 Exp. 2, Fac. Sci. Paris, 1963.Google Scholar
[T1] Takemoto, F., Stable vector bundles on algebraic surfaces I, Nagoya Math. J., 47 (1972), 29–48.CrossRefGoogle Scholar
[T2] Takemoto, F., Stable vector bundles on algebraic surfaces II, Nagoya Math. J, 52 (1973), 173–195.CrossRefGoogle Scholar
[W] Walter, C. H., Components of the stack of torsion-free sheaves of rank-2 on ruled surfaces, Math. Ann., 301 (1995), 699–716.CrossRefGoogle Scholar