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- W4310826016 abstract "We show that if $Z$ is a local complete intersection subvariety of a smooth complex variety $X$, of pure codimension $r$, then $Z$ has $k$-rational singularities if and only if $widetilde{alpha}(Z)>k+r$, where $widetilde{alpha}(Z)$ is the minimal exponent of $Z$. We also characterize this condition in terms of the Hodge filtration on the intersection cohomology Hodge module of $Z$. Furthermore, we show that if $Z$ has $k$-rational singularities, then the Hodge filtration on the local cohomology sheaf $mathcal{H}^r_Z(mathcal{O}_X)$ is generated at level $dim(X)-lceil widetilde{alpha}(Z)rceil-1$ and, assuming that $kgeq 1$ and $Z$ is singular, of dimension $d$, that $mathcal{H}^k(underline{Omega}_Z^{d-k})neq 0$. All these results have been known for hypersurfaces in smooth varieties." @default.
- W4310826016 created "2022-12-18" @default.
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- W4310826016 date "2022-12-04" @default.
- W4310826016 modified "2023-10-17" @default.
- W4310826016 title "The minimal exponent and $k$-rationality for local complete intersections" @default.
- W4310826016 doi "https://doi.org/10.48550/arxiv.2212.01898" @default.
- W4310826016 hasPublicationYear "2022" @default.
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