Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-15T09:42:04.389Z Has data issue: false hasContentIssue false
  • English
  • Français

Moduli of endomorphisms of semistable vector bundles over a compact Riemann surface

Published online by Cambridge University Press:  18 May 2009

L. Brambila Paz
L. Brambila Paz
Affiliation:
Departmento de MatemáticasUniversidad Autónoma Metropolitana, Iztapalapa Av. La Purisima y Michoacán, Iztapalapa, Apdo. Postal 55–534México, D. F. C. P. 09340
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Mumford and Suominen in [8] and Newstead in [11] have considered the moduli problem of classifying the endomorphisms of finite-dimensional vector spaces. Using similar ideas we consider the moduli problem for endomorphisms of indecomposable semistable vector bundles over a compact connected Riemann surface of genus g ≥ 2.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 1 , January 1990 , pp. 1 - 12
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

1.Atiyah, M. F., Complex analytic connections in fibre bundles, Trans, Amer. Math. Soc. 85 (1957), 181–207.Google Scholar
2.Brambila, L., Endomorphisms of vector bundles over a compact Riemann surface: 2-dimensional case, in Several complex variables (Pitman, 1985), 90–95.Google Scholar
3.Brambila, L., Algebras of endomorphisms of semistable vector bundles over a compact Riemann surface, Reportes de investigación 1986, Universidad Autónoma Metropolitana Mexico.Google Scholar
4.Brambila, L., Existence of universal extensions, preprint.Google Scholar
5.Harder, G. and Narasimhan, M. S., On the cohomology group of moduli space of vector bundles on curves, Math. Ann. 212 (1975), 215–248.CrossRefGoogle Scholar
6.Harstshorne, R., Algebraic geometry, (Springer Verlag, 1977).CrossRefGoogle Scholar
7.Lange, H., Universal families of extensions, J. Algebra 83 (1983), 101–112.CrossRefGoogle Scholar
8.Mumford, D. and Suominen, K., Introduction to the theory of moduli, 5th Nordic Summer School in Math. Algebraic Geometry, Oslo, 1970.Google Scholar
9.Narasimham, M. S. and Ramanan, S., Moduli of vector bundles on a compact Riemann surface, Ann. of Math. (2) 89 (1969), 14–51.CrossRefGoogle Scholar
10.Narasimhan, M. S. and Seshadri, C. S., Holomorphic vector bundles on a compact Riemann surface, Math. Ann. 155 (1964), 69–80.Google Scholar
11.Newstead, P. E., Lectures on introduction to moduli problems and orbit space (Tata Institute of Fundamental Research, Bombay, 1978).Google Scholar
12.Ramanan, S., Moduli of vector bundles over an algebraic curve, Math. Ann. 200 (1973), 69–84.Google Scholar
13.Shatz, S. S., The decomposition and specialization of algebra families of vector bundles. Compositio Math. 35 (1977), 163–187.Google Scholar