TY - JOUR

T1 - THE DU BOIS COMPLEX OF A HYPERSURFACE AND THE MINIMAL EXPONENT

AU - Mustata, Mircea

AU - Olano, Sebastián

AU - Popa, Mihnea

AU - Witaszek, Jakub

N1 - Funding Information:
for 1 i p 1. The assertions in (ii) are immediate consequences. (The vanishing statement also follows from Corollary 3.8, and holds for an arbitrary isolated singularity.) Acknowledgments. M.M. was partially supported by National Science Foundation (NSF) grants DMS-2001132 and DMS-1952399, M.P. by NSF grant DMS-2040378, and J.W. by NSF grant DMS-2101897.
Publisher Copyright:
© 2023 Duke University Press. All rights reserved.

PY - 2023

Y1 - 2023

N2 - We study the Du Bois complex ΩZ of a hypersurface Z in a smooth complex algebraic variety in terms of its minimal exponent eα.Z/. 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 eα.Z/ > p C 1, then the canonical morphism ΩpZ ! Ωp _Z is an isomorphism, where Ωp _Z 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 eα.Z/

AB - We study the Du Bois complex ΩZ of a hypersurface Z in a smooth complex algebraic variety in terms of its minimal exponent eα.Z/. 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 eα.Z/ > p C 1, then the canonical morphism ΩpZ ! Ωp _Z is an isomorphism, where Ωp _Z 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 eα.Z/

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U2 - 10.1215/00127094-2022-0074

DO - 10.1215/00127094-2022-0074

M3 - Article

AN - SCOPUS:85161863436

SN - 0012-7094

VL - 172

SP - 1411

EP - 1436

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 7

ER -