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Deformation invariance of plurigenera

Published online by Cambridge University Press:  22 January 2016

Hajime Tsuji*
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ohokayama, Megro 152-8551, Japan, [email protected]
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Abstract

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We prove the invariance of plurigenera under smooth projective deformations in full generality.

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[1] Demailly, J.P., Regularization of closed positive currents and intersection theory, J. of Alg. Geom., 1 (1992), 361409.Google Scholar
[2] Demailly, J.P., Peternell, T. and Schneider, M., Pseudo-effective line bundles on compact Kähler manifolds, math. AG/0006025 (2000).Google Scholar
[3] Iitaka, S., Deformations of complex surfaces, II, J. Math. Soc. of Japan, 22 (1970), 247261.Google Scholar
[4] Kawamata, Y., Deformations of canonical singularities, J. of Amer. Math. Soc., 12 (1999), 8592.Google Scholar
[5] Kollár, J., Higher direct images of dualizing sheaves, I, Ann. of Math. (2), 123 (1986), no. 1, 1142.Google Scholar
[6] Krantz, S., Function Theory of Several Complex Variables, John Wiley and Sons, 1982.Google Scholar
[7] Lelong, P., Fonctions Plurisousharmoniques et Formes Differentielles Positives, Gordon and Breach, 1968.Google Scholar
[8] Manivel, L., Un theoreme de prolongement L2 de sections holomorphes d’un fibre hermitien [An L2 extension theorem for the holomorphic sections of a Hermitian bundle], Math. Z., 212 (1993), no. 1, 107122.Google Scholar
[9] Nakamura, I., Complex parallelisable manifolds and their small deformations, J. Differential Geom., 10 (1975), 85112.Google Scholar
[10] Nakayama, N., Invariance of plurigenera of algebraic varieties under minimal model conjectures, Topology, 25, 237251.Google Scholar
[11] Nakayama, N., Invariance of plurigenera of algebraic varieties, RIMS preprint (1998).Google Scholar
[12] Ohsawa, T., On the extension of L2 holomorphic functions V, effects of generalization, Nagoya Math. J., 161 (2001), 121.Google Scholar
[13] Ohsawa, T. and Takegoshi, K., L2-extension of holomorphic functions, Math. Z., 195 (1987), 197204.Google Scholar
[14] Siu, Y.-T., Invariance of plurigenera, Invent. Math., 134 (1998), 661673.Google Scholar
[15] Tsuji, H., Analytic Zariski decomposition, Proc. of Japan Acad., 61 (1992), 161163.Google Scholar
[16] Tsuji, H., Existence and Applications of Analytic Zariski Decompositions, Analysis and Geometry in Several Complex Variables (Komatsu and Kuranishi ed.), Trends in Math., 253271, Birkhäuser, 1999.Google Scholar
[17] Tian, G., On a set of polarized Kähler metrics on algebraic manifolds, J. Differential Geom., 32 (1990), 99130.Google Scholar