Alexander Bednarek : On Miyaoka-Yau Inequalities and Weil-Petersson Metrics

The classical Miyaoka-Yau inequality is a constraint on Kahler-Einstein manifolds where equality is equivalent to being a complex space form. We discuss how the Kahler-Ricci flow can provide several extensions of the inequality to non-KE manifolds, and the connection with the slope stability of the holomorphic tangent bundle. Finally, we display a connection with the Weil-Petersson metric, a form measuring the variation of complex structures, and that equality in the extended Miyaoka-Yau inequality is equivalent to being a holomorphic fibre bundle. This is recent work: arXiv.2609.06451.