turkmath.org

Miyaoka-Yau inequality is a classical inequality that concerns the Chern numbers of a minimal algebraic surface of general type, together with a rigid geometric characterization of the case of equality. Namely, an algebraic surface satisfies equality if and only if it is a quotient of the unit ball. Corresponding result for higher-dimensional smooth varieties with ample canonical class also dates back to Yau. In this talk, I will present a recent paper by (Greb, Kebekus, Peternell, Taji) in which the authors prove the Miyaoka-Yau inequality for all minimal varieties of general type and generalize the ball quotient characterization to this context.