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.
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.
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
@article{AIF_2014__64_1_203_0, author = {Taji, Behrouz}, title = {Birational positivity in dimension $4$}, journal = {Annales de l'Institut Fourier}, pages = {203--216}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {1}, year = {2014}, doi = {10.5802/aif.2845}, zbl = {1326.14093}, mrnumber = {3330547}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2845/} }
TY - JOUR AU - Taji, Behrouz TI - Birational positivity in dimension $4$ JO - Annales de l'Institut Fourier PY - 2014 SP - 203 EP - 216 VL - 64 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2845/ DO - 10.5802/aif.2845 LA - en ID - AIF_2014__64_1_203_0 ER -
%0 Journal Article %A Taji, Behrouz %T Birational positivity in dimension $4$ %J Annales de l'Institut Fourier %D 2014 %P 203-216 %V 64 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2845/ %R 10.5802/aif.2845 %G en %F AIF_2014__64_1_203_0
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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