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The Miyaoka-Yau inequality and the delta invariant for Fano varieties II -soliton case-
Abstract
Inspired by recent work of Inoue and Hallam-Lahdili, we prove an equivariant Miyaoka-Yau inequality with a correction term for smooth Fano manifolds admitting Kähler-Ricci solitons. It recovers the usual Miyaoka-Yau inequality in the Kähler-Einstein case. Our proof uses weighted equivariant Bogomolov-Gieseker and Langer inequalities for torsion-free sheaves, together with a weighted slope estimate for the canonical extension sheaf. We also construct toric examples showing that the existence of a soliton implies neither weighted semistability of the canonical extension sheaf nor nonnegativity of the equivariant Miyaoka-Yau number.
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BibTeX
@misc{hisamoto2026miyaokayau,
title = {{The Miyaoka-Yau inequality and the delta invariant for Fano varieties II -soliton case-}},
author = {Tomoyuki Hisamoto and Masataka Iwai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38137},
eprint = {2610.38137},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38137},
}
RIS
TY - UNPB
TI - The Miyaoka-Yau inequality and the delta invariant for Fano varieties II -soliton case-
AU - Tomoyuki Hisamoto
AU - Masataka Iwai
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38137
UR - https://arxiv.org/abs/2610.38137
AB - Inspired by recent work of Inoue and Hallam-Lahdili, we prove an equivariant Miyaoka-Yau inequality with a correction term for smooth Fano manifolds admitting Kähler-Ricci solitons. It recovers the usual Miyaoka-Yau inequality in the Kähler-Einstein case. Our proof uses weighted equivariant Bogomolov-Gieseker and Langer inequalities for torsion-free sheaves, together with a weighted slope estimate for the canonical extension sheaf. We also construct toric examples showing that the existence of a soliton implies neither weighted semistability of the canonical extension sheaf nor nonnegativity of the equivariant Miyaoka-Yau number.
ER -