Stability of tangent bundle on the moduli space of stable bundles on a curve

Abstract

In this paper, we prove that the tangent bundle of the moduli space $\cSU_C(r,d)$ of stable bundles of rank $r>2$ and of fixed determinant of degree $d$ (such that $(r,d)=1$), on a smooth projective curve $C$ is always stable, in the sense of Mumford-Takemoto. This verifies a well-known conjecture, and is related to a conjectural existence of a Kähler-Einstein metric on Fano varieties with Picard number one.

arXiv commentRevised version, Lemma 4.3,4.4 added

References in corpus (1)

• K-stability and Kähler-Einstein metrics

Cited by in corpus (2)

• Fano manifolds and stability of tangent bundles
• Kähler-Einstein metrics and higher alpha-invariants