Comptes Rendus
Analytic geometry
From Hörmander’s L 2 -estimates to partial positivity
Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 169-179.

In this article, using a twisted version of Hörmander’s L 2 -estimate, we give new characterizations of notions of partial positivity, which are uniform q-positivity and RC-positivity. We also discuss the definition of uniform q-positivity for singular Hermitian metrics.

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DOI: 10.5802/crmath.168
Classification: 32U05
Keywords: $L^2$-estimates, $q$-positivity, RC-positivity

Takahiro Inayama 1

1 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {From {H\"ormander{\textquoteright}s} $L^2$-estimates to partial positivity},
     journal = {Comptes Rendus. Math\'ematique},
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     publisher = {Acad\'emie des sciences, Paris},
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     year = {2021},
     doi = {10.5802/crmath.168},
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Takahiro Inayama. From Hörmander’s $L^2$-estimates to partial positivity. Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 169-179. doi : 10.5802/crmath.168. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.168/

[1] Aldo Andreotti; Hans Grauert Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. Fr., Volume 90 (1962), pp. 193-259 | DOI | Numdam | Zbl

[2] Bo Berndtsson Prekopa’s theorem and Kiselman’s minimum principle for plurisubharmonic functions, Math. Ann., Volume 312 (1998) no. 4, pp. 785-792 | DOI | MR | Zbl

[3] Dario Cordero-Erausquin On Berndtsson’s generalization of Prékopa’s theorem, Math. Z., Volume 249 (2005) no. 2, pp. 401-410 | DOI | MR | Zbl

[4] Jean-Pierre Demailly Complex analytic and differential geometry (http://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf)

[5] Jean-Pierre Demailly Estimations L 2 pour l’opérateur ¯ d’un fibré vectoriel holomorphe semi-positif au dessus d’une variété Kählérienne complète, Ann. Sci. Éc. Norm. Supér., Volume 15 (1982), pp. 457-511 | DOI | Numdam | Zbl

[6] Jean-Pierre Demailly Analytic methods in algebraic geometry, Surveys of Modern Mathematics, 1, International Press; Higher Education Press, 2012 | MR | Zbl

[7] Fusheng Deng; Jiafu Ning; Zhiwei Wang Characterizations of plurisubharmonic functions (2019) (https://arxiv.org/abs/1910.06518)

[8] Fusheng Deng; Jiafu Ning; Zhiwei Wang; Xiangyu Zhou Positivity of holomorphic vector bundles in terms of L p -conditions of ¯ (2020) (https://arxiv.org/abs/2001.01762)

[9] Fusheng Deng; Huiping Zhang; Xiangyu Zhou Positivity of direct images of positively curved volume forms, Math. Z., Volume 278 (2014) no. 1-2, pp. 347-362 | DOI | MR | Zbl

[10] Lars Hörmander L 2 estimates and existence theorems for the ¯ operator, Acta Math., Volume 113 (1965), pp. 89-152 | DOI | MR | Zbl

[11] Genki Hosono; Takahiro Inayama A converse of Hörmander’s L 2 -estimate and new positivity notions for vector bundles, Sci. China, Math. (2020) | DOI

[12] Takahiro Inayama Nakano positivity of singular Hermitian metrics and vanishing theorems of Demailly-Nadel-Nakano type (2020) (https://arxiv.org/abs/2004.05798)

[13] Andras Prekopa On logarithmic concave measures and functions, Acta Sci. Math., Volume 34 (1973), pp. 335-343 | MR | Zbl

[14] Xiaokui Yang RC-positivity, rational connectedness and Yau’s conjecture, Camb. J. Math., Volume 6 (2018) no. 2, pp. 183-212 | DOI | MR | Zbl

[15] Xiaokui Yang A partial converse to the Andreotti–Grauert theorem, Compos. Math., Volume 155 (2019) no. 1, pp. 89-99 | DOI | MR | Zbl

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