The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisors

2025/07/11 by Masataka Iwai, Satoshi Jinnouchi, Iwai, Masataka +3 · 2 citations
Mathematics · #math.AG #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.2507.08522

Abstract

We establish the Miyaoka-Yau inequality for n-dimensional projective klt varieties with big canonical divisor K_X: (2(n+1)\widehatc₂(X) - n \widehatc₁(X)²) ⋅ ⟨ c₁(K_X)^n-2 ⟩ ≥ 0. We also prove the Miyaoka-Yau inequality for K-semistable projective klt varieties with big anticanonical divisor -K_X. As part of our approach, we define the non-pluripolar product ⟨ α₁ ⋯ α_p ⟩ on singular varieties, and establish the Bogomolov-Gieseker type inequality for ⟨ α^n-1 ⟩-semistable Higgs sheaves with respect to a big class α.

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