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Deformations of Canonical Bundle for Smooth Weakly Kähler Morphisms
Abstract
Let π: \mathcal X \rightarrow Δbe a smooth proper family of compact complex manifolds such that the central fiber \mathcal X_0 is Kähler. Then all the fibers close to 0 are Kähler and π is a weakly Kähler morphism, even if \mathcal X is not a Kähler space. In this paper we show that if dim \mathcal X_0 = 4 and K_{\mathcal X_0} is nef, then K_{\mathcal X_t} is nef for all t in a neighborhood of the origin.
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BibTeX
@misc{wang2026deformations,
title = {{Deformations of Canonical Bundle for Smooth Weakly Kähler Morphisms}},
author = {Liqingjing Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18507},
eprint = {2609.18507},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18507},
}
RIS
TY - UNPB
TI - Deformations of Canonical Bundle for Smooth Weakly Kähler Morphisms
AU - Liqingjing Wang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18507
UR - https://arxiv.org/abs/2609.18507
AB - Let π: \mathcal X \rightarrow Δbe a smooth proper family of compact complex manifolds such that the central fiber \mathcal X_0 is Kähler. Then all the fibers close to 0 are Kähler and π is a weakly Kähler morphism, even if \mathcal X is not a Kähler space. In this paper we show that if dim \mathcal X_0 = 4 and K_{\mathcal X_0} is nef, then K_{\mathcal X_t} is nef for all t in a neighborhood of the origin.
ER -