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 that is independent of positivity results for tangent sheaves.

v2: 40 pages, final version. Significant changes in the exposition following the referees' suggestions; main results unchanged

References in corpus (3)

• Klt varieties with trivial canonical class -- Holonomy, differential forms, and fundamental groups
• The Miyaoka-Yau inequality and uniformisation of canonical models
• Generic positivity and applications to hyperbolicity of moduli spaces

Cited by in corpus (6)

• The Miyaoka-Yau inequality and uniformisation of canonical models
• On the stability of extensions of tangent sheaves on Kähler-Einstein Fano / Calabi-Yau pairs
• Bogomolov's inequality and Higgs sheaves on normal varieties in positive characteristic
• Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs
• Miyaoka-Yau inequality for compact Kähler manifolds with semi-positive canonical bundle
• On the structure of a log smooth pair in the equality case of the Bogomolov-Gieseker inequality