Abstract
We study the Du Bois complex of a hypersurface Z in a smooth complex algebraic variety in terms of its minimal exponent . The latter is an invariant of singularities, defined as the negative of the greatest root of the reduced Bernstein–Sato polynomial of Z, and refining the log-canonical threshold. We show that if , then the canonical morphism is an isomorphism, where is the pth associated graded piece of the Du Bois complex with respect to the Hodge filtration. On the other hand, if Z is singular and , we obtain non-vanishing results for some higher cohomologies of .
Citation
Mircea Mustaţă. Sebastián Olano. Mihnea Popa. Jakub Witaszek. "The Du Bois complex of a hypersurface and the minimal exponent." Duke Math. J. 172 (7) 1411 - 1436, 15 May 2023. https://doi.org/10.1215/00127094-2022-0074
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