Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T20:14:42.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Moduli spaces of the stable vector bundles over abelian surfaces

Published online by Cambridge University Press:  22 January 2016

Hiroshi Umemura
Hiroshi Umemura*
Affiliation:
Nagoya University
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.

Let X be a projective non-singular variety and H an ample line bundle on X. The moduli space of H-stable vector bundles exists by Maruyama [4]. If X is a curve defined over C, the structure of the moduli space (or its compactification) M(X, d, r) of stable vector bundles of degree d and rank r on X is studied in detail. It is known that the variety M(X, d, r) is irreducible. Let L be a line bundle of degree d and let M(X, L, r) denote the closed subvariety of M(X, d, r) consisting of all the stable bundles E with det E = L.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 77 , February 1980 , pp. 47 - 60
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1980

References

[1] Barth, W., Moduli of vector bundles on the projective plans, Inventiones Math., 42 (1977), 63–91.CrossRefGoogle Scholar
[2] Maruyama, M., Stable vector bundles on an algebraic surface, Nagoya Math. J., 58 (1975), 25–68.Google Scholar
[3] Maruyama, M., Openness of a family of torsion free sheaves, J. Math. Kyoto Univ., 16 (1976), 627–637.Google Scholar
[4] Maruyama, M., Moduli of stable sheaves, I, II, J. Math. Kyoto Univ., 17 (1977), 91–126, preprint.Google Scholar
[5] Maruyama, M., Boundedness of semi-stable sheaves of small rank, preprint.Google Scholar
[6] Matsumura, H., On algebraic groups of birational transformations, Lincei Rend. Sc. fis. e nat., 34 (1963), 151–155.Google Scholar
[7] Morikawa, H., A note on holomorphic vector bundles over complex tori, Nagoya Math. J., 41 (1971), 101–106.CrossRefGoogle Scholar
[8] Mukai, S., Duality between D(X) and D(X̂) with its application to the Picard sheaves, preprint.Google Scholar
[9] Mumford, D., Introduction to algebraic geometry, to appear.Google Scholar
[10] Mumford, D., Abelian Varieties, Oxford Univ. Press 1970.Google Scholar
[11] Takemoto, F., Stable vector bundles on algebraic surfaces II, Nagoya Math. J., 52 (1973), 29–48.CrossRefGoogle Scholar
[12] Ueno, K., Classification theory of algebraic varieties and compact complex spaces, Lecture notes in Math. 439, Springer (1975).Google Scholar
[13] Umemura, H., Some result in the theory of vector bundles, Nagoya Math. J., 52 (1973), 173–195.CrossRefGoogle Scholar
[14] Umemura, H., Stable vector bundles with numerically trivial Chern classes over hyper-elliptic surfaces, Nagoya Math. J., 59 (1975), 107–134.Google Scholar
[15] Umemura, H., On a certain type of vector bundles over an abelian variety, Nagoya Math. J., 64 (1976), 31–45.CrossRefGoogle Scholar
[16] Umemura, H., On a property of symmetric products of a curve of genus 2, Proc. Int. Symp. Algebraic Geometry, Kyoto (1977), 709–721.Google Scholar
[17] Weil, A., Variétés abéliennes et courbes algebriques, Hermann, Paris 1948.Google Scholar
[18] Weil, A., Zum Beweis des Torellishen Satzes, Nachr. Akad. Wiss. Göttingen 1957.Google Scholar