[Idéaux de Hodge pour des -diviseurs : approche birationnelle]
Nous développons la théorie des idéaux de Hodge pour les -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 -filtration dans un autre article.
We develop the theory of Hodge ideals for -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 -filtration is analyzed in a sequel.
Accepté le :
Publié le :
DOI : 10.5802/jep.94
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
Mircea Mustaţǎ 1 ; Mihnea Popa 2
CC-BY 4.0
@article{JEP_2019__6__283_0,
author = {Mircea Musta\c{t}ǎ and Mihnea Popa},
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},
volume = {6},
year = {2019},
doi = {10.5802/jep.94},
mrnumber = {3959075},
zbl = {07070281},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.94/}
}
TY - JOUR
AU - Mircea Mustaţǎ
AU - Mihnea Popa
TI - Hodge ideals for $\protect \mathbf{Q}$-divisors: birational approach
JO - Journal de l’École polytechnique — Mathématiques
PY - 2019
SP - 283
EP - 328
VL - 6
PB - École polytechnique
UR - https://jep.centre-mersenne.org/articles/10.5802/jep.94/
DO - 10.5802/jep.94
LA - en
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%D 2019
%P 283-328
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%I École polytechnique
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Mircea Mustaţǎ; Mihnea Popa. 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. https://jep.centre-mersenne.org/articles/10.5802/jep.94/
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