Stability of tangent bundle on the moduli space of stable bundles on a curve
Stability of tangent bundle on the moduli space of stable bundles on a curve
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曲线上稳定丛模空间上切丛的稳定性
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发表时间：
2011
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通讯作者：
J. Iyer
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作者：
J. Iyer
本文证明了光滑射影曲线$C上的模空间$\CSU_C(r，d)$在Mumford-Takemoto意义下是稳定的。这验证了一个著名的猜想，并与一个关于Picard数为1的Fano簇的Kahler-Einstein度量的猜想的存在有关。
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 Kahler-Einstein metric on Fano varieties with Picard number one.