Hostname: page-component-6bb9c88b65-s7dlb Total loading time: 0 Render date: 2025-07-26T09:53:53.087Z Has data issue: false hasContentIssue false
  • English
  • Français

COHERENCE OF MULTIPLIER SUBMODULE SHEAVES ON GENERIC COMPLEX TORI

Part of: Compact analytic spaces Cycles and subschemes Holomorphic fiber spaces (Co)homology theory

Published online by Cambridge University Press:  30 June 2025

HUI YANG Open the ORCID record for HUI YANG [Opens in a new window]
HUI YANG*
Affiliation:
School of Mathematical Sciences https://ror.org/02v51f717Peking University No.5 Yiheyuan Road, Haidian District 100871, Beijing P.R.China
*
yanghui@amss.ac.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove the coherence of multiplier submodule sheaves associated with Griffiths semi-positive singular hermitian metrics over holomorphic vector bundles on complex manifolds which have no nontrivial subvarieties, such as generic complex tori.

Keywords

multiplier submodule sheafcoherenceGriffiths positivityholomorphic vector bundle

MSC classification

Primary: 14F18: Multiplier ideals 14C30: Transcendental methods, Hodge theory , Hodge conjecture 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results 32J25: Transcendental methods of algebraic geometry

Information

Type
Article
Information
Nagoya Mathematical Journal , First View , pp. 1 - 8
Check for updates
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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.)

Article purchase

Temporarily unavailable

References

Berndtsson, B. and Păun, M., Bergman kernels and the pseudoeffectivity of relative canonical bundles , Duke Math. J. 145 (2008), 341–378.10.1215/00127094-2008-054CrossRefGoogle Scholar
Campana, F., Demailly, J. P. and Verbitsky, M., Compact Kähler 3-manifolds without nontrivial subvarieties , Algebr. Geom. 1 (2014), 131–139.10.14231/AG-2014-007CrossRefGoogle Scholar
de Cataldo, M. A. A., Singular Hermitian metrics on vector bundles , J. Reine Angew. Math. 502 (1998), 93–122.10.1515/crll.1998.091CrossRefGoogle Scholar
Demailly, J. P., Complex Analytic and Differential Geometry. Available at http://www-fourier.ujf-grenoble.fr/~demailly/books.html.Google Scholar
Demailly, J. P. and Skoda, H., “Relations entre les notions de positivités de P. A. Griffiths et de S. Nakano pour les fibrés vectoriels” in P. Lelong and H. Skoda, (eds.), Séminaire Pierre Lelong-Henri Skoda (Analyse), Années 1978/79, Lecture Notes in Mathematics, 822, Springer, Berlin, 1980, 304–309.10.1007/BFb0097764CrossRefGoogle Scholar
Hosono, G., Approximations and examples of singular Hermitian metrics on vector bundles , Ark. Mat. 55 (2017), 131–153.10.4310/ARKIV.2017.v55.n1.a6CrossRefGoogle Scholar
Hosono, G. and Inayama, T., A converse of Hörmander’s ${L}^2$ -estimate and new positivity notions for vector bundles , Sci. China Math. 64 (2021), 1745–1756.10.1007/s11425-019-1654-9CrossRefGoogle Scholar
Inayama, T., Nakano positivity of singular Hermitian metrics and vanishing theorems of Demailly-Nadel-Nakano type , Algebr. Geom. 9 (2020), 69–92.Google Scholar
Inayama, T., Singular Hermitian metrics with isolated singularities , Nagoya Math. J. 248 (2022), 980–989.10.1017/nmj.2022.16CrossRefGoogle Scholar
Iwai, M., Nadel-Nakano vanishing theorems of vector bundles with singular Hermitian metrics , Ann. Fac. Sci. Toulouse Math. (6) 30 (2021), 63–81.10.5802/afst.1666CrossRefGoogle Scholar
Nadel, A. M., Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature , Proc. Nat. Acad. Sci. U.S.A. 86 (1989), 7299–7300 and Ann. of Math. 132 (1990), 549–596.10.1073/pnas.86.19.7299CrossRefGoogle ScholarPubMed
Păun, M. and Takayama, S., Positivity of twisted relative pluricanonical bundles and their direct images , J. Algebraic Geom. 27 (2018), 211–272.10.1090/jag/702CrossRefGoogle Scholar
Raufi, H., Singular Hermitian metrics on holomorphic vector bundles , Ark. Mat. 53 (2015), 359–382.10.1007/s11512-015-0212-4CrossRefGoogle Scholar
Verbitsky, M., Coherent sheaves on generic compact tori, CRM Proceedings & Lecture Notes, 38, American Mathematical Society, Providence, RI, 2004, 229–249.10.1090/crmp/038/11CrossRefGoogle Scholar
Zou, Y., Note on the singular Hermitian metrics with analytic singularities, preprint, arXiv:2209.05053, 2022.Google Scholar