×

zbMATH — the first resource for mathematics

The singularity of the canonical model of compact Kähler manifolds. (English) Zbl 0625.14004
Let X be a compact Kähler manifold whose canonical ring \({\mathcal R}:=\oplus _{m\geq 0}H^ 0(X,{\mathcal O}_ x(mK_ x))\quad is\) finitely generated. Then there exists an effective \({\mathbb{Q}}\)-divisor \(\Delta\) on \(S:=\Pr oj {\mathcal R}\) such that (S,\(\Delta)\) is log-terminal.

MSC:
14C20 Divisors, linear systems, invertible sheaves
53C55 Global differential geometry of Hermitian and Kählerian manifolds
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Fujita, T.: A relative version of Kawamata-Viehweg’s vanishing theorem. Preprint 1984
[2] Fujita, T.: Remarks on the semi-stable reduction theorem. Preprint 1986
[3] Kawamata, Y.: Characterization of abelian varieties. Compos. Math.43, 253-276 (1981) · Zbl 0471.14022
[4] Kawamata, Y.: The cone of curves of algebraic varieties. Ann. Math.119, 603-633 (1984) · Zbl 0544.14009
[5] Kawamata, Y.: Pluricanonical systems on minimal algebraic varieties. Invent. Math.79, 567-588 (1985) · Zbl 0593.14010
[6] Kawamata, Y., Matsuda, K., Matsuki, K.: Introduction to the minimal model problem. In: Algebraic geometry. Sendai, 1985, T. Oda (ed.), pp. 283-360. Advanced Studies in Pure Math. 10. Tokyo: Kinokuniya and Amsterdam: North-Holland 1987
[7] Koll?r, J.: Higher direct images of dualizing sheaves. II. Ann. Math.124, 171-202 (1986) · Zbl 0605.14014
[8] Mori, S.: Classification of higher dimensional varieties. To appear in the Proceedings of AMS Summer Institute, Bowdoin 1985 · Zbl 0589.14005
[9] Nakayama, N.: The lower semi-continuity of the plurigenera of complex varieties. In: Algebraic geometry. Sendai, 1985, T. Oda (ed.), pp. 551-590. Advanced Studies in Pure Math. 10. Tokyo: Kinokuniya and Amsterdam: North-Holland 1987
[10] Nakayama, N.: On Weierstrass models. To appear · Zbl 0699.14049
[11] Reid, M.: Canonical 3-folds. In: G?om?trie alg?brique, angers, 1979. A. Beauville (ed.), pp. 273-310. Alphen aan den Rijn: Sifthoff and Noordhoff 1980
[12] Viehweg, E.: Weak positivity and the additivity of the Kodaira dimension for certain fiber spaces. In: Algebraic and analytic varieties, S. Iitaka (ed.), pp. 329-353. Advanced Studies in Pure Math. 1, Tokyo: Kinokuniya and Amsterdam: North-Holland 1983
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.