Illinois Journal of Mathematics

On the Kähler structures over Quot schemes, II

Indranil Biswas and Harish Seshadri

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Let $X$ be a compact connected Riemann surface of genus $g$, with $g\geq 2$, and let $\mathcal{O}_{X}$ denote the sheaf of holomorphic functions on $X$. Fix positive integers $r$ and $d$ and let $\mathcal{Q}(r,d)$ be the Quot scheme parametrizing all torsion coherent quotients of $\mathcal{O}^{\oplus r}_{X}$ of degree $d$. We prove that $\mathcal{Q}(r,d)$ does not admit a Kähler metric whose holomorphic bisectional curvatures are all nonnegative.

Article information

Illinois J. Math., Volume 58, Number 3 (2014), 689-695.

Received: 30 January 2014
Revised: 24 March 2015
First available in Project Euclid: 9 September 2015

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Zentralblatt MATH identifier

Primary: 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05] 32Q10: Positive curvature manifolds 14H81: Relationships with physics


Biswas, Indranil; Seshadri, Harish. On the Kähler structures over Quot schemes, II. Illinois J. Math. 58 (2014), no. 3, 689--695. doi:10.1215/ijm/1441790384.

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