https://neckpinch.com/authors/masataka-iwai/New arXiv papers by Masataka Iwai, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.38137/arxiv:2610.38137Wed, 28 Oct 2026 00:00:00 GMTTomoyuki Hisamoto, Masataka Iwai — 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.Ricci solitonsKähler–Ricci solitonsEinstein metricsKähler geometryKähler–Einstein & K-stability https://neckpinch.com/papers/2607.25181/arxiv:2607.25181Tue, 28 Jul 2026 00:00:00 GMTTomoyuki Hisamoto, Masataka Iwai — We establish the following Miyaoka-Yau inequality for any n-dimensional klt Fano variety X, possibly K-unstable, in terms of its delta invariant: (2(n+1)c₂(X)−n c₁(X)²)· c₁(X)ⁿ⁻² ≥ −n (1-min\1,δ(X)\)² · c₁(X)ⁿ. Furthermore, inspired by recent work of Inoue and Hallam-Lahdili, we formulate and prove an equivariant version of this inequality in the soliton setting, in which the Chern classes and the delta invariant are replaced by the equivariant Chern classes and the weighted delta invariant, respectively. As a consequence, we obtain the equivariant Miyaoka-Yau inequality for every smooth Fano manifold admitting a Kähler-Ricci soliton.Ricci solitonsKähler–Ricci solitonsKähler geometryStability & uniquenessKähler–Einstein & K-stabilityAnalytic minimal model program