Hostname: page-component-7dd5485656-tbj44 Total loading time: 0 Render date: 2025-10-31T19:38:58.273Z Has data issue: false hasContentIssue false
  • English
  • Français

Deformation invariance of plurigenera

Published online by Cambridge University Press:  22 January 2016

Hajime Tsuji
Hajime Tsuji*
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ohokayama, Megro 152-8551, Japan, tsuji@math.titech.ac.jp
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.

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

Keywords

32J25

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 166 , June 2002 , pp. 117 - 134
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), 361–409.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), 247–261.Google Scholar
[4] Kawamata, Y., Deformations of canonical singularities, J. of Amer. Math. Soc., 12 (1999), 85–92.Google Scholar
[5] Kollár, J., Higher direct images of dualizing sheaves, I, Ann. of Math. (2), 123 (1986), no. 1, 11–42.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, 107–122.Google Scholar
[9] Nakamura, I., Complex parallelisable manifolds and their small deformations, J. Differential Geom., 10 (1975), 85–112.Google Scholar
[10] Nakayama, N., Invariance of plurigenera of algebraic varieties under minimal model conjectures, Topology, 25, 237–251.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), 1–21.Google Scholar
[13] Ohsawa, T. and Takegoshi, K., L2-extension of holomorphic functions, Math. Z., 195 (1987), 197–204.Google Scholar
[14] Siu, Y.-T., Invariance of plurigenera, Invent. Math., 134 (1998), 661–673.Google Scholar
[15] Tsuji, H., Analytic Zariski decomposition, Proc. of Japan Acad., 61 (1992), 161–163.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., 253–271, Birkhäuser, 1999.Google Scholar
[17] Tian, G., On a set of polarized Kähler metrics on algebraic manifolds, J. Differential Geom., 32 (1990), 99–130.Google Scholar