Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-25T01:01:35.632Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical criteria for certain fiber spaces to be birationally trivial

Published online by Cambridge University Press:  22 January 2016

Jin-Xing Cai
Jin-Xing Cai*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China, cai@math.pku.edu.cn
Rights & Permissions [Opens in a new window]

Abstract

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 f: X → B be a fiber space over a curve B whose general fiber F belongs to one of the following type: 1) F is of general type and satisfying some mild conditions, 2) F is with trivial canonical sheaf. In this note, a numerical characterization for f: X → B to be birationally trivial is given.

Keywords

14D05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 168 , 2002 , pp. 93 - 103
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[1] Beauville, A., L’application canonique pour les surfaces de type général, Invent. Math., 55 (1979), 121–140.CrossRefGoogle Scholar
[2] Beauville, A., L’inegalite pg ≥ 2q - 4 pour les surfaces de type général, Appendice à O. Debarre: “Inégalités numériques pour les surfaces de type général”, Bull. Soc. Math. France, 110 (1982), 343–346.Google Scholar
[3] Barth, W., Peters, C. and Ven, A. Van de, Compact complex surfaces, Ergeb. Math. Grenzgeb., 1984.CrossRefGoogle Scholar
[4] Bogomolov, F., Holomorphic tensors and vector bundles on projective varieties, Math. USSR, Izv. 13 (1979), 499–555.CrossRefGoogle Scholar
[5] Fujita, T., On Kaehler fibre spaces over curves, J. Math. Soc. Japan, 30 (1978), 779–794.CrossRefGoogle Scholar
[6] Kollár, J., Subadditivity of the Kodaira dimension: fibers of general type, Alg. Geom. Sendai, 1985, Adv. Studies Pure Math., 10 (1987), 361–398.Google Scholar
[7] Levine, M., Deformation of irregular threefolds, Lect. Notes in Math. 947, Springer (1982), pp. 269–286.Google Scholar
[8] Luo, T., Global 2-forms on regular 3-folds of general type, Duke Math. Jour., 71 (1993), 859–869.CrossRefGoogle Scholar
[9] Mabuchi, T., Invariant β and uniruled threefolds, J. Math. Kyoto Univ., 22 (1982), 503–554.Google Scholar
[10] Mori, S., Classification of higher-dimensional varieties, Proceedings of Symposia in Pure Math., 46 (1987), 269–331.CrossRefGoogle Scholar