Weak transcendental holomorphic Morse inequalities on compact Kähler manifolds
[Inégalités de Morse holomorphes transcendantes faibles sur les variétés kähleriennes]
Xiao, Jian1
1 Institute of Mathematics, Fudan University 200433 Shanghai (China)
Annales de l'Institut Fourier, Tome 65 (2015) no. 3, pp. 1367-1379.

Les inégalités de Morse holomorphes transcendantes caractérisent la positivité des classes cohomologiques transcendantes de type (1,1). Dans ce papier, nous démontrons une version faible d’une conjecture de Demailly sur les inégalités de Morse holomorphes transcendantes sur les variétés kähleriennes. En conséquence, nous améliorons partiellement un résultat de Boucksom-Demailly-Paun-Peternell.

Transcendental holomorphic Morse inequalities aim at characterizing the positivity of transcendental cohomology classes of type (1,1). In this paper, we prove a weak version of Demailly’s conjecture on transcendental Morse inequalities on compact Kähler manifolds. And as a consequence, we partially improve a result of Boucksom-Demailly-Paun-Peternell.

DOI : 10.5802/aif.2959
Classification : 32C30, 32Q15
Keywords: Transcendental holomorphic Morse inequalities, positivity of cohomology classes, Kähler manifolds
Mot clés : Inégalités de Morse holomorphes transcendantes, positivité des classes cohomologiques, variétés kähleriennes
Xiao, Jian 1

1 Institute of Mathematics, Fudan University 200433 Shanghai (China) 
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Xiao, Jian. Weak transcendental holomorphic Morse inequalities on compact Kähler manifolds. Annales de l'Institut Fourier, Tome 65 (2015) no. 3, pp. 1367-1379. doi : 10.5802/aif.2959. http://www.numdam.org/articles/10.5802/aif.2959/

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