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A Complex Structure on T2× S4: The Genus-One Case of Calabi's Problem
Abstract
We construct a complex structure on T2× S4, giving an affirmative answer to the genus-one case of Calabi's problem. The resulting compact complex threefold is non-Kähler and admits no biholomorphic product decomposition.
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BibTeX
@misc{gao2026complex,
title = {{A Complex Structure on $T^2\times S^4$: The Genus-One Case of Calabi's Problem}},
author = {Min Gao and Zizhou Tang and Wenjiao Yan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06067},
eprint = {2610.06067},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06067},
}
RIS
TY - UNPB
TI - A Complex Structure on T^2× S^4: The Genus-One Case of Calabi's Problem
AU - Min Gao
AU - Zizhou Tang
AU - Wenjiao Yan
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06067
UR - https://arxiv.org/abs/2610.06067
AB - We construct a complex structure on T^2× S^4, giving an affirmative answer to the genus-one case of Calabi's problem. The resulting compact complex threefold is non-Kähler and admits no biholomorphic product decomposition.
ER -