By a canonical (resp. terminal) weak -Fano -fold we mean a normal projective one with at worst canonical (resp. terminal) singularities on which the anti-canonical divisor is -Cartier, nef and big. For a canonical weak -Fano -fold , we show that there exists a terminal weak -Fano -fold , being birational to , such that the -th anti-canonical map defined by is birational for all . As an intermediate result, we show that for any -Mori fiber space of a canonical weak -Fano -fold, the -th anti-canonical map defined by is birational for all .
Par variété de dimension trois canonique (resp. terminale) faiblement -Fano, nous entendons une variété normale projective avec au plus des singularités canoniques (resp. terminales) sur laquelle le diviseur anticanonique est -Cartier, nef et big. Pour une variété de dimension trois canonique faiblement -Fano , nous montrons qu’il existe une variété de dimension trois terminale faiblement -Fano birationnelle à , de sorte que l’application pluri-anticanonique définie par est birationnelle sur son image pour tous les . Comme un résultat intermédiaire, nous montrons que pour n’importe quelle -fibration de Mori d’une variété de dimension trois canonique faiblement -Fano, l’application pluri-anticanonique définie par est birationnelle sur son image pour tous les .
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Keywords: Fano variety, pluri-anti-canonical map
Mot clés : variétés de Fano, l’application pluri-anticanonique
Chen, Meng 1; Jiang, Chen 2
@article{AIF_2020__70_6_2473_0, author = {Chen, Meng and Jiang, Chen}, title = {On the anti-canonical geometry of weak $\protect \mathbb{Q}${-Fano} threefolds {II}}, journal = {Annales de l'Institut Fourier}, pages = {2473--2542}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {70}, number = {6}, year = {2020}, doi = {10.5802/aif.3367}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3367/} }
TY - JOUR AU - Chen, Meng AU - Jiang, Chen TI - On the anti-canonical geometry of weak $\protect \mathbb{Q}$-Fano threefolds II JO - Annales de l'Institut Fourier PY - 2020 SP - 2473 EP - 2542 VL - 70 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3367/ DO - 10.5802/aif.3367 LA - en ID - AIF_2020__70_6_2473_0 ER -
%0 Journal Article %A Chen, Meng %A Jiang, Chen %T On the anti-canonical geometry of weak $\protect \mathbb{Q}$-Fano threefolds II %J Annales de l'Institut Fourier %D 2020 %P 2473-2542 %V 70 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3367/ %R 10.5802/aif.3367 %G en %F AIF_2020__70_6_2473_0
Chen, Meng; Jiang, Chen. On the anti-canonical geometry of weak $\protect \mathbb{Q}$-Fano threefolds II. Annales de l'Institut Fourier, Volume 70 (2020) no. 6, pp. 2473-2542. doi : 10.5802/aif.3367. https://aif.centre-mersenne.org/articles/10.5802/aif.3367/
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