Hodge ideals for Q-divisors: birational approach
[Idéaux de Hodge pour des Q-diviseurs : approche birationnelle]
Mustaţǎ, Mircea1 ; Popa, Mihnea2
1 Department of Mathematics, University of Michigan Ann Arbor, MI 48109, USA
2 Department of Mathematics, Northwestern University 2033 Sheridan Road, Evanston, IL 60208, USA
Journal de l’École polytechnique - Mathématiques, Tome 6 (2019), pp. 283-328.

Nous développons la théorie des idéaux de Hodge pour les Q-diviseurs à l’aide de log résolutions, généralisant notre précédent travail sur les hypersurfaces réduites. Nous obtenons des critères de (non) trivialité locale et un théorème d’annulation global, ainsi que d’autres analogues de résultats standard de la théorie des idéaux multiplicateurs, et nous en déduisons un nouveau théorème d’annulation local. Nous analysons la relation avec la V-filtration dans un autre article.

We develop the theory of Hodge ideals for Q-divisors by means of log resolutions, extending our previous work on reduced hypersurfaces. We prove local (non-)triviality criteria and a global vanishing theorem, as well as other analogues of standard results from the theory of multiplier ideals, and we derive a new local vanishing theorem. The connection with the V-filtration is analyzed in a sequel.

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DOI : 10.5802/jep.94
Classification : 14F10, 14J17, 32S25, 14F17
Keywords: Hodge ideals, D-modules, Hodge filtration, vanishing theorems, minimal exponent
Mot clés : Idéaux de Hodge, D-modules, filtration de Hodge, théorèmes d’annulation, exposant minimal
Mustaţǎ, Mircea 1 ; Popa, Mihnea 2

1 Department of Mathematics, University of Michigan Ann Arbor, MI 48109, USA
2 Department of Mathematics, Northwestern University 2033 Sheridan Road, Evanston, IL 60208, USA 
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Mustaţǎ, Mircea; Popa, Mihnea. Hodge ideals for ${\protect \bf Q}$-divisors: birational approach. Journal de l’École polytechnique - Mathématiques, Tome 6 (2019), pp. 283-328. doi : 10.5802/jep.94. http://www.numdam.org/articles/10.5802/jep.94/

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