PreprintarXiv licencearXiv
Boundedness of polarized log Calabi-Yau fibrations
Abstract
We investigate the boundedness problem for log Calabi-Yau fibrations whose bases and general fibers are bounded. We improve the results in arXiv:2504.05243 from birational boundedness to actual boundedness, which confirms a conjecture of Birkar and Hacon when the boundary coefficients belong to a fixed finite rational set. We also get a new proof for the birational boundedness result in arXiv:2504.05243 which is substantially more conceptual.
Related
- Singular Kähler--Ricci shrinkers and polarized Fano fibrations
- Calabi flow on polarized Kähler surfaces
- Chern bounds and tangent geometry of polarized Calabi-Yau threefolds
- A Pluripotential-Theoretic Approach to Finiteness of Polarized Calabi--Yau Manifolds
- Shrinking Kähler-Ricci solitons on toric fano fibrations
BibTeX
@misc{zhu2026boundedness,
title = {{Boundedness of polarized log Calabi-Yau fibrations}},
author = {Haoran Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13178},
eprint = {2610.13178},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13178},
}
RIS
TY - UNPB
TI - Boundedness of polarized log Calabi-Yau fibrations
AU - Haoran Zhu
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13178
UR - https://arxiv.org/abs/2610.13178
AB - We investigate the boundedness problem for log Calabi-Yau fibrations whose bases and general fibers are bounded. We improve the results in arXiv:2504.05243 from birational boundedness to actual boundedness, which confirms a conjecture of Birkar and Hacon when the boundary coefficients belong to a fixed finite rational set. We also get a new proof for the birational boundedness result in arXiv:2504.05243 which is substantially more conceptual.
ER -