Birational positivity in dimension 4
[Positivité birational en dimension 4]
Taji, Behrouz
Annales de l'Institut Fourier, Tome 64 (2014), p. 203-216 / Harvested from Numdam

Dans cet article, nous montrons que pour une variété projective lisse, X, de dimension au plus 4 et de dimension de Kodaira non négative, la dimension de Kodaira des sous-faisceaux cohérents de Ω p est majorée par la dimension de Kodaira de X. Cela implique la finitude du groupe fondamental de X lorsque la dimension de Kodaira de X est nulle et sa caractéristique holomorphe d’Euler est non nulle.

In this paper we prove that for a nonsingular projective variety of dimension at most 4 and with non-negative Kodaira dimension, the Kodaira dimension of coherent subsheaves of Ω p is bounded from above by the Kodaira dimension of the variety. This implies the finiteness of the fundamental group for such an X provided that X has vanishing Kodaira dimension and non-trivial holomorphic Euler characteristic.

Publié le : 2014-01-01
DOI : https://doi.org/10.5802/aif.2845
Classification:  14J35,  14E30
Mots clés: dimension de Kodaira, variétés avec la dimension de Kodaira nulle, théorie du modéle minimal
@article{AIF_2014__64_1_203_0,
     author = {Taji, Behrouz},
     title = {Birational positivity in dimension $4$},
     journal = {Annales de l'Institut Fourier},
     volume = {64},
     year = {2014},
     pages = {203-216},
     doi = {10.5802/aif.2845},
     zbl = {06387272},
     mrnumber = {3330547},
     zbl = {1326.14093},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2014__64_1_203_0}
}
Taji, Behrouz. Birational positivity in dimension $4$. Annales de l'Institut Fourier, Tome 64 (2014) pp. 203-216. doi : 10.5802/aif.2845. http://gdmltest.u-ga.fr/item/AIF_2014__64_1_203_0/

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