# zbMATH — the first resource for mathematics

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