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arXiv · 2610.38137

The Miyaoka-Yau inequality and the delta invariant for Fano varieties II -soliton case-

Tomoyuki Hisamoto·Masataka Iwai
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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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Tomoyuki Hisamoto, Masataka Iwai. 2026-10-28. The Miyaoka-Yau inequality and the delta invariant for Fano varieties II -soliton case-. https://arxiv.org/abs/2610.38137

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