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Smoothness criterion for Fano orbifolds and bases of Lagrangian fibrations

  • Zhiyu Liu
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Abstract

We establish a smoothness criterion for Fano varieties with quotient singularities. As an application, we show that if X→ B is a Lagrangian fibration from a compact hyper-Kähler manifold and B has quotient singularities, then B is a projective space.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026smoothness,
  title = {{Smoothness criterion for Fano orbifolds and bases of Lagrangian fibrations}},
  author = {Zhiyu Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20496},
  eprint = {2610.20496},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20496},
}
RIS
TY  - UNPB
TI  - Smoothness criterion for Fano orbifolds and bases of Lagrangian fibrations
AU  - Zhiyu Liu
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20496
UR  - https://arxiv.org/abs/2610.20496
AB  - We establish a smoothness criterion for Fano varieties with quotient singularities. As an application, we show that if X→ B is a Lagrangian fibration from a compact hyper-Kähler manifold and B has quotient singularities, then B is a projective space.
ER  -