Orbifold stability and Miyaoka–Yau inequality for minimal pairs

Abstract

After establishing suitable notions of stability and Chern classes for singular pairs, we use Kähler–Einstein metrics with conical and cuspidal singularities to prove the slope semistability of orbifold tangent sheaves of minimal log canonical pairs of log general type. We then proceed to prove the Miyaoka–Yau inequality for all minimal pairs with standard coefficients. Our result in particular provides an alternative proof of the abundance theorem for threefolds, which is independent of positivity results for cotangent sheaves established by Miyaoka.