Dans cet article, nous montrons que pour une variété projective lisse, , de dimension au plus et de dimension de Kodaira non négative, la dimension de Kodaira des sous-faisceaux cohérents de est majorée par la dimension de Kodaira de . Cela implique la finitude du groupe fondamental de lorsque la dimension de Kodaira de 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 is bounded from above by the Kodaira dimension of the variety. This implies the finiteness of the fundamental group for such an provided that has vanishing Kodaira dimension and non-trivial holomorphic Euler characteristic.
@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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