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 - 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 -