Birational positivity in dimension 4
Annales de l'Institut Fourier, Volume 64 (2014) no. 1, pp. 203-216.

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.

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.

DOI: 10.5802/aif.2845
Classification: 14J35, 14E30
Keywords: Kodaira dimension, varieties of Kodaira dimension zero, minimal model theory
Mot clés : dimension de Kodaira, variétés avec la dimension de Kodaira nulle, théorie du modéle minimal
Taji, Behrouz 1

1 McGill University The Department of Mathematics Burnside Hall, Room 1031 805 Sherbrooke W. Montreal, QC, H3A 0B9 (Canada)
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Taji, Behrouz. Birational positivity in dimension $4$. Annales de l'Institut Fourier, Volume 64 (2014) no. 1, pp. 203-216. doi : 10.5802/aif.2845. https://aif.centre-mersenne.org/articles/10.5802/aif.2845/

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