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Positivity of Smooth Currents on Singular Spaces

  • Duc-Thai Do
  • Duc-Viet Vu
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Abstract

We study two notions of positivity for smooth currents on singular spaces. We show that they are not equivalent by establishing a necessary condition on the fourth Whitney cones. We also construct an explicit compact normal projective variety X and a real smooth (1,1)-form T on X such that T has local smooth ddc-potentials and is a Kähler current, but T is not a positive form (hence not Hermitian).

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Cite

BibTeXRIS
BibTeX
@misc{do2026positivity,
  title = {{Positivity of Smooth Currents on Singular Spaces}},
  author = {Duc-Thai Do and Duc-Viet Vu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04335},
  eprint = {2609.04335},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04335},
}
RIS
TY  - UNPB
TI  - Positivity of Smooth Currents on Singular Spaces
AU  - Duc-Thai Do
AU  - Duc-Viet Vu
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04335
UR  - https://arxiv.org/abs/2609.04335
AB  - We study two notions of positivity for smooth currents on singular spaces. We show that they are not equivalent by establishing a necessary condition on the fourth Whitney cones. We also construct an explicit compact normal projective variety X and a real smooth (1,1)-form T on X such that T has local smooth ddc-potentials and is a Kähler current, but T is not a positive form (hence not Hermitian).
ER  -