Stability of tangent bundles of minimal algebraic varieties. (English) Zbl 0698.14008

Tsuji, Hajime

Topology 27, No. 4, 429-442 (1988).

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.

Reviewer: L.Picco Botta

MSC:

14E30	Minimal model program (Mori theory, extremal rays)
14F05	Sheaves, derived categories of sheaves, etc. (MSC2010)

Keywords:

Miyaoka-Yau inequality; minimal variety; Chern classes; Kähler-Einstein metric