Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Numerical invariants for bundles on blow-ups

Authors: E. Ballico and E. Gasparim
Journal: Proc. Amer. Math. Soc. 130 (2002), 23-32
MSC (2000): Primary 14J60, 14F05.
Published electronically: May 3, 2001
MathSciNet review: 1855615
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


We suggest an effective procedure to calculate numerical invariants for rank two bundles over blown-up surfaces. We study the moduli spaces ${\mathcal M}_j$ of rank two bundles on the blown-up plane splitting over the exceptional divisor as ${\mathcal O}(j) \oplus {\mathcal O}(-j).$ We use the numerical invariants to give a topological decomposition of ${\mathcal M}_j.$

References [Enhancements On Off] (What's this?)

  • 1. Ballico, E. and Gasparim, E. Vector Bundles on a Neighborhood of an exceptional curve and Elementary Transformations, to appear
  • 2. Robert Friedman and John W. Morgan, On the diffeomorphism types of certain algebraic surfaces. II, J. Differential Geom. 27 (1988), no. 3, 371–398. MR 940111
  • 3. Robin Hartshorne, Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. MR 0463157
  • 4. Lang, S. Algebra, Addison-Wesley Pub. Co. 3rd. Ed. (1993)
  • 5. Elizabeth Gasparim, Holomorphic bundles on 𝒪(-𝓀) are algebraic, Comm. Algebra 25 (1997), no. 9, 3001–3009. MR 1458743,
  • 6. Elizabeth Gasparim, Rank two bundles on the blow-up of 𝐶², J. Algebra 199 (1998), no. 2, 581–590. MR 1489927,
  • 7. Gasparim, E. On the Topology of Holomorphic Bundles, Boletim da Sociedade Paranaense de Matemática, 18, 1-7 (1998) CMP 2000:15
  • 8. Gasparim, E. Chern Classes of Bundles on Rational Surfaces, Politécnico di Torino, Rapporto Interno N.30 (1998)
  • 9. Gasparim, E. Moduli of Bundles on the Blown-up Plane, math.AG/9810106

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14J60, 14F05.

Retrieve articles in all journals with MSC (2000): 14J60, 14F05.

Additional Information

E. Ballico
Affiliation: Department of Mathematics, University of Trento, 38050 Povo (TN), Italy

E. Gasparim
Affiliation: Departamento de Matematica, Universidade Federal de Pernambuco, 50670/901 Recife (PE), Brasil

Received by editor(s): September 1, 1999
Received by editor(s) in revised form: May 29, 2000
Published electronically: May 3, 2001
Additional Notes: The first author was partially supported by MURST (Italy)
The second author was partially supported by CNPQ (Brasil)
Communicated by: Michael Stillman
Article copyright: © Copyright 2001 American Mathematical Society