Hodge ideals for Q-divisors: birational approach
Mircea Mustaţǎ; Mihnea Popa
Journal de l'École polytechnique — Mathématiques, Volume 6 (2019), p. 283-328

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.

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.

Received : 2018-11-19
Accepted : 2019-05-13
Published online : 2019-08-19
DOI : https://doi.org/10.5802/jep.94
Classification:  14F10,  14J17,  32S25,  14F17
Keywords: Hodge ideals, D-modules, Hodge filtration, vanishing theorems, minimal exponent
@article{JEP_2019__6__283_0,
     author = {Mircea Musta\c t\v a and Mihnea Popa},
     title = {Hodge ideals for $\protect \mathbf{Q}$-divisors: birational~approach},
     journal = {Journal de l'\'Ecole polytechnique --- Math\'ematiques},
     publisher = {\'Ecole polytechnique},
     volume = {6},
     year = {2019},
     pages = {283-328},
     doi = {10.5802/jep.94},
     language = {en},
     url = {https://jep.centre-mersenne.org/item/JEP_2019__6__283_0}
}
Mustaţǎ, Mircea; Popa, Mihnea. Hodge ideals for $\protect \mathbf{Q}$-divisors: birational approach. Journal de l'École polytechnique — Mathématiques, Volume 6 (2019) pp. 283-328. doi : 10.5802/jep.94. https://jep.centre-mersenne.org/item/JEP_2019__6__283_0/

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