PreprintCC BY 4.0arXiv
On Miyaoka-Yau Inequalities and Weil-Petersson Metrics
Abstract
We use the Kähler-Ricci flow to give alternate proofs of several known Miyaoka-Yau inequalities and slope semi-stabilities, in particular, for the case of compact Kähler manifolds with semi-ample canonical line bundles and K-semistable Fano manifolds. Moreover, when the canonical line bundle is semi-ample, and the Kodaira dimension is n−1, we prove the Miyaoka-Yau quantity is equal to the intersection of the Weil-Petersson metric and the Fubini-Study metric on the canonical model. Consequently, equality holds in the Miyaoka-Yau inequality if and only if the pluricanonical map is a holomorphic fibre bundle.
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BibTeX
@misc{bednarek2026miyaokayau,
title = {{On Miyaoka-Yau Inequalities and Weil-Petersson Metrics}},
author = {Alexander Bednarek},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06451},
eprint = {2609.06451},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06451},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Miyaoka-Yau Inequalities and Weil-Petersson Metrics
AU - Alexander Bednarek
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06451
UR - https://arxiv.org/abs/2609.06451
AB - We use the Kähler-Ricci flow to give alternate proofs of several known Miyaoka-Yau inequalities and slope semi-stabilities, in particular, for the case of compact Kähler manifolds with semi-ample canonical line bundles and K-semistable Fano manifolds. Moreover, when the canonical line bundle is semi-ample, and the Kodaira dimension is n−1, we prove the Miyaoka-Yau quantity is equal to the intersection of the Weil-Petersson metric and the Fubini-Study metric on the canonical model. Consequently, equality holds in the Miyaoka-Yau inequality if and only if the pluricanonical map is a holomorphic fibre bundle.
ER -