Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-15T01:57:34.678Z Has data issue: false hasContentIssue false

The components of mKv for threefolds with x(V) = 0

Published online by Cambridge University Press:  24 October 2008

P. M. H. Wilson
Affiliation:
Department of Pure Mathematics, University of Cambridge, Cambridge CB2 1SB, U.K.

Abstract

For V a complex algebraic threefold with k( V) = 0 and having at least one minimal model (for definition, see below), we show that (except possibly in one rather special case) the components of an effective divisor mKv are birationally ruled surfaces.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1985

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]Hochster, M. and Eagon, J. A.. Cohen-Macaulay rings, invariant theory, and the generic perfection of determinantal loci. Amer. J. Math. 93 (1971), 10201058.CrossRefGoogle Scholar
[2]Kawamata, Y.. Elementary contractions of algebraic 3-folds. Annals of Math. 119 (1984), 95110.CrossRefGoogle Scholar
[3]Kawamata, Y.. The cone of curves of algebraic varieties. Annals of Math. 119, (1984), 603633.CrossRefGoogle Scholar
[4]Kawamata, Y.. Pluricanonical systems on minimal algebraic varieties. (To appear.)Google Scholar
[5]Milnor, J.. Singular Points of Complex Hypersurfaces. Ann. of Math. Studies, no. 61 (Princeton University Press, 1968).Google Scholar
[6]Mori, S.. Threefolds whose canonical bundles are not numerically effective. Ann. of Math. 116 (1982), 133176.CrossRefGoogle Scholar
[7]Mumford, D.. Enriques' classification of surfaces in char p: I. In Global Analysis: Papers in Honour of K. Kodaira, ed. Spencer, D. C. and Iyanaga, S. (University of Tokyo Press 1969), pp. 325340.Google Scholar
[8]Reid, M.. Canonical 3-folds. In Journées de Géométrie Algébrique, Juillèt 1979, ed. Beauville, A. (Sijthoff & Noordhoff, 1980), pp. 273310.Google Scholar
[9]Reid, M.. Minimal models of canonical threefolds. In Algebraic Varieties and Analytic Varieties, ed. Iitaka, S. and Morikawa, H.. Advanced Studies in Pure Math., no. 1 (Kinokuniya, Tokyo and North-Holland, Amsterdam, 1983), pp. 131180.CrossRefGoogle Scholar
[10]Wilson, P. M. H.. On regular threefolds with k = 0. Invent. math. 76 (1984), 345355.CrossRefGoogle Scholar