Stability of tangent bundles of minimal algebraic varieties (Q912162)

A smooth algebraic variety X over \({\mathbb{C}}\) is called minimal if X has at worst canonical singularities and if the canonical divisor \(K_ X\) of X is \({\mathbb{Q}}\)-Cartier and numerically effective. The author proves that for an n-dimensional smooth minimal variety X the tangent bundle TX is \(K_ X\)-semistable and the Chern classes of X satisfy a Miyaoka-Yau-type inequality. The proof is based on the construction of a Kähler-Einstein metric on X with a pole of rational order along an ample divisor: it follows that TX can be obtained as a limit of a sequence of semistable \({\mathbb{Q}}\)-vector bundles.