For projective klt varieties with big canonical or anticanonical divisor, the Miyaoka-Yau Chern class inequality holds when intersections are taken with the non-pluripolar product.
On the Miyaoka-Yau inequality for manifolds with nef anti-canonical line bundle
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abstract
Based on the recent work of K.~Zhang, we discuss the Miyaoka-Yau type inequality for projective manifolds with nef anti-canonical line bundle, assuming the lower bound of the delta-invariant introduced by Fujita and Odaka.
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The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisors
For projective klt varieties with big canonical or anticanonical divisor, the Miyaoka-Yau Chern class inequality holds when intersections are taken with the non-pluripolar product.