PreprintCC BY 4.0arXiv
The Kawatani--Okawa conjecture in dimensions three and four
Abstract
We prove that a smooth projective threefold or fourfold whose bounded derived category admits no nontrivial semiorthogonal decomposition has nef canonical divisor, confirming the Kawatani--Okawa conjecture in these dimensions. The proof combines the classification of extremal contractions with constructions of admissible subcategories. In dimension four, we refine the descriptions of isolated surface fibers and construct exceptional objects supported on certain fibers.
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BibTeX
@misc{wu2026kawataniokawa,
title = {{The Kawatani--Okawa conjecture in dimensions three and four}},
author = {Dongjian Wu and Nantao Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39838},
eprint = {2610.39838},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39838},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Kawatani--Okawa conjecture in dimensions three and four
AU - Dongjian Wu
AU - Nantao Zhang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39838
UR - https://arxiv.org/abs/2610.39838
AB - We prove that a smooth projective threefold or fourfold whose bounded derived category admits no nontrivial semiorthogonal decomposition has nef canonical divisor, confirming the Kawatani--Okawa conjecture in these dimensions. The proof combines the classification of extremal contractions with constructions of admissible subcategories. In dimension four, we refine the descriptions of isolated surface fibers and construct exceptional objects supported on certain fibers.
ER -