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Weighted multiplier ideals of reduced divisors

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We use methods from birational geometry to study the Hodge and weight filtrations on the localization along a hypersurface. We focus on the lowest piece of the Hodge filtration of the submodules arising from the weight filtration. This leads to a sequence of ideal sheaves called weighted multiplier ideals. The last ideal of this sequence is a multiplier ideal (and a Hodge ideal), and we prove that the first is the adjoint ideal. We also study the local and global properties of weighted multiplier ideals and their applications to singularities of hypersurfaces of smooth varieties.

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Acknowledgements

I would like to thank Mihnea Popa for his constant support during the project, and Tommaso de Fernex, Lawrence Ein, Sándor Kovács, Mircea Mustaţă, and Mingyi Zhang for very helpful discussions. Finally, I am thankful to the anonymous referee for valuable comments and especially for pointing out previously known results about the Hodge theoretic interpretation of the adjoint ideal.

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  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Sebastián Olano

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  1. Sebastián Olano
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Communicated by Roseline Periyanayagam.

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Olano, S. Weighted multiplier ideals of reduced divisors. Math. Ann. 384, 1091–1126 (2022). https://doi.org/10.1007/s00208-021-02306-3

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