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Peer-reviewedCC BYAlgebra & Number Theory

Injectivity and vanishing for the Du Bois complexes of isolated singularities

  • Mihnea Popa1
  • Wanchun Shen1
  • Anh Duc Vo1
  1. 1Department of Mathematics, Harvard University, Cambridge, MA, United States
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Abstract

We prove an injectivity theorem for the cohomology of the Du Bois complexes of varieties with isolated singularities.We use this to deduce vanishing statements for the cohomologies of higher Du Bois complexes of such varieties.Besides some extensions and conjectures in the nonisolated case, we also provide analogues for intersection complexes.p X can be identified with the sheaf of Kähler differentials p X for certain p.Along

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Cite

BibTeXRIS
BibTeX
@article{popa2026injectivity,
  title = {{Injectivity and vanishing for the Du Bois complexes of isolated singularities}},
  author = {Mihnea Popa and Wanchun Shen and Anh Duc Vo},
  journal = {Algebra \& Number Theory},
  year = {2026},
  month = may,
  doi = {10.2140/ant.2026.20.1235},
  url = {https://doi.org/10.2140/ant.2026.20.1235},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Injectivity and vanishing for the Du Bois complexes of isolated singularities
AU  - Mihnea Popa
AU  - Wanchun Shen
AU  - Anh Duc Vo
PY  - 2026
DA  - 2026/05/26
JO  - Algebra & Number Theory
DO  - 10.2140/ant.2026.20.1235
UR  - https://doi.org/10.2140/ant.2026.20.1235
AB  - We prove an injectivity theorem for the cohomology of the Du Bois complexes of varieties with isolated singularities.We use this to deduce vanishing statements for the cohomologies of higher Du Bois complexes of such varieties.Besides some extensions and conjectures in the nonisolated case, we also provide analogues for intersection complexes.p X can be identified with the sheaf of Kähler differentials p X for certain p.Along
SN  - 1937-0652
SN  - 1944-7833
ER  -