Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-30T21:59:32.780Z Has data issue: false hasContentIssue false
  • English
  • Français

Birational pairs according to S. Iitaka

Published online by Cambridge University Press:  24 October 2008

D. Dicks
D. Dicks
Affiliation:
Mathematics Institute, Warwick University
Get access Rights & Permissions [Opens in a new window]

Extract

This paper is largely inspired by the work and results of Iitaka in [6]. The study undertaken is of pairs X & C, up to birational equivalence, where X is a projective, non-singular surface and C is a reduced curve on X. In [6] Iitaka gives a classification of &-minimal pairs and introduces the important idea of the #-minimal model. The classification of &-minimal pairs given here is a slight improvement on that of Iitaka on account of the use of Mori theory in place of more classical methods. Before the classification in Section 3 we have included a section on the uniqueness of the &-minimal model which does not occur in the work of Iitaka.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 1 , July 1987 , pp. 59 - 69
Copyright
Copyright © Cambridge Philosophical Society 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Barth, W., Peters, C. and Van de Ven, A.. Compact Complex Surfaces. (Springer-Verlag, 1984.)CrossRefGoogle Scholar
[2] Coble, A.. Algebraic Geometry & Theta Functions. A.M.S. Coll. Publ. vol. 10 (American Mathematical Society, 1929).Google Scholar
[3] Coolidge, J. L.. A Treatise on Algebraic Plane Curves. (Oxford University Press, 1928.)Google Scholar
[4] Demazure, M., Pinkham, H. and Teissier, B.. Séminaire sur les Singularités des Surfaces. Lecture Notes in Math. vol. 777 (Springer-Verlag, 1980).CrossRefGoogle Scholar
[5] Dolgachev, I.. Weyl groups and cremona transformations. Preprint.Google Scholar
[6] Iitaka, S.. On irreducible plane curves. Saitama Math. J. 1 (1983), 47–63.Google Scholar
[7] Manin, Y.. Cubic Forms. (North-Holland, 1974.)Google Scholar
[8] Mori, S.. Threefolds whose canonical bundles are not effective. Proc. Nat. Acad. Sci. U.S.A. 77 (1980), 3125–3126.CrossRefGoogle Scholar
[9] Suzuki, S.. Birational geometry of birational pairs. Commentarii Mathematici Universitis Sancti Pauli, vol. 32, no. 1, 1983.Google Scholar
[10] Tsunoda, S. and M. Miyanishi. The structure of open algebraic surfaces 2. Class, of Alg. and Analytic Manifolds, Birkhäuser, 499–545.Google Scholar
[11] Reid, M.. Surfaces of small degree. Warwick preprint, to appear in Math. Annalen.Google Scholar
[12] Gang, Xiao. Hyperelliptic surfaces of general type with K 2 < 4χ, Shanghai preprint.Google Scholar
[13] Gang, Xiao. Algebraic surfaces with high canonical degree. Shanghai preprint, to appear in Math. Annalen.Google Scholar