We consider singular -acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is - or -ruled or the surface is up to isomorphism one of two exceptional surfaces of Kodaira dimension zero. For both exceptional surfaces the Kodaira dimension of the smooth locus is zero and the singular locus consists of a unique point of type and respectively.
On considère des surfaces -acycliques singulières dont la partie lisse n’est pas de type général. On démontre que si les singularités sont topologiquement rationnelles, alors soit la partie lisse est réglée par ou , soit la surface est l’une de deux surfaces exceptionnelles de dimension de Kodaira zéro. Pour les deux surfaces exceptionnelles, la dimension de Kodaira de la partie lisse est zéro, il n’y a qu’un seul point singulier et la singularité est de type ou , respectivement.
Keywords: Acyclic surface, homology plane, exceptional Q-homology plane
Mot clés : surface acyclique
@article{AIF_2011__61_2_745_0, author = {Palka, Karol}, title = {Exceptional singular $\mathbb{Q}$-homology planes}, journal = {Annales de l'Institut Fourier}, pages = {745--774}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {2}, year = {2011}, doi = {10.5802/aif.2628}, zbl = {1236.14054}, mrnumber = {2895072}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2628/} }
TY - JOUR AU - Palka, Karol TI - Exceptional singular $\mathbb{Q}$-homology planes JO - Annales de l'Institut Fourier PY - 2011 SP - 745 EP - 774 VL - 61 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2628/ DO - 10.5802/aif.2628 LA - en ID - AIF_2011__61_2_745_0 ER -
%0 Journal Article %A Palka, Karol %T Exceptional singular $\mathbb{Q}$-homology planes %J Annales de l'Institut Fourier %D 2011 %P 745-774 %V 61 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2628/ %R 10.5802/aif.2628 %G en %F AIF_2011__61_2_745_0
Palka, Karol. Exceptional singular $\mathbb{Q}$-homology planes. Annales de l'Institut Fourier, Volume 61 (2011) no. 2, pp. 745-774. doi : 10.5802/aif.2628. http://www.numdam.org/articles/10.5802/aif.2628/
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