THE DU BOIS COMPLEX OF A HYPERSURFACE AND THE MINIMAL EXPONENT

Mircea Mustata, Sebastián Olano, Mihnea Popa, Jakub Witaszek

Research output: Contribution to journalArticlepeer-review

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Abstract

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/

Original languageEnglish (US)
Pages (from-to)1411-1436
Number of pages26
JournalDuke Mathematical Journal
Volume172
Issue number7
DOIs
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics

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