Hodge ideals for Q-divisors: birational approach
[Idéaux de Hodge pour des Q-diviseurs : approche birationnelle]
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 : https://doi.org/10.5802/jep.94
Classification : 14F10,  14J17,  32S25,  14F17
Mots clés : Idéaux de Hodge, D-modules, filtration de Hodge, théorèmes d’annulation, exposant minimal
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     author = {Musta\c{t}ǎ, Mircea and Popa, Mihnea},
     title = {Hodge ideals for $\protect \mathbf{Q}$-divisors: birational~approach},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {283--328},
     publisher = {Ecole polytechnique},
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Mustaţǎ, Mircea; Popa, Mihnea. Hodge ideals for $\protect \mathbf{Q}$-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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