no. 5
On a generalized canonical bundle formula for generically finite morphisms
[Sur une formule de fibré canonique généralisée pour les morphismes génériquement finis]
Han, Jingjun1, 2, 3 ; Liu, Wenfei4
1 Department of Mathematics, The University of Utah, Salt Lake City, UT 84112, (USA)
2 Mathematical Sciences Research Institute, Berkeley, CA 94720, (USA)
3 Shanghai Center for Mathematical Sciences, Fudan University, Jiangwan Campus, Shanghai, 200438, (China)
4 Xiamen University School of Mathematical Sciences Siming South Road 422 Xiamen, Fujian 361005 China
Annales de l'Institut Fourier, Tome 71 (2021) no. 5, pp. 2047-2077.

Nous prouvons une formule de fibré canonique pour des morphismes génériquement finis dans le cadre de paires généralisées (avec ℝ-coefficients). Cela complète la formule de fibré canonique de Filipazzi pour les morphismes à fibres connectées. Elle est ensuite appliquée pour obtenir une formule de sous-jonction pour les centres log canoniques de paires généralisées. Comme une autre application, nous montrons que l’image d’une paire généralisée canonique anti-nef log a la structure d’une paire généralisée canonique log numériquement triviale. Cela implique un résultat de Chen–Zhang. Au passage, nous prouvons que les ensembles convexes de type de Shokurov pour les diviseurs log canoniques anti-nef sont en effet des ensembles polyédriques rationnels.

We prove a canonical bundle formula for generically finite morphisms in the setting of generalized pairs (with ℝ-coefficients). This complements Filipazzi’s canonical bundle formula for morphisms with connected fibres. It is then applied to obtain a subadjunction formula for log canonical centers of generalized pairs. As another application, we show that the image of an anti-nef log canonical generalized pair has the structure of a numerically trivial log canonical generalized pair. This readily implies a result of Chen–Zhang. Along the way we prove that the Shokurov type convex sets for anti-nef log canonical divisors are indeed rational polyhedral sets.

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Révisé le :
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DOI : 10.5802/aif.3437
Classification : 14E30, 14N30
Keywords: generalized pair, canonical bundle formula, subadjunction
Mot clés : paire généralisée, formule de fibré canonique, sous-adjonction
Han, Jingjun 1, 2, 3 ; Liu, Wenfei 4

1 Department of Mathematics, The University of Utah, Salt Lake City, UT 84112, (USA)
2 Mathematical Sciences Research Institute, Berkeley, CA 94720, (USA)
3 Shanghai Center for Mathematical Sciences, Fudan University, Jiangwan Campus, Shanghai, 200438, (China)
4 Xiamen University School of Mathematical Sciences Siming South Road 422 Xiamen, Fujian 361005 China
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Han, Jingjun; Liu, Wenfei. On a generalized canonical bundle formula for generically finite morphisms. Annales de l'Institut Fourier, Tome 71 (2021) no. 5, pp. 2047-2077. doi : 10.5802/aif.3437. https://aif.centre-mersenne.org/articles/10.5802/aif.3437/

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