Illinois Journal of Mathematics

On the Kähler structures over Quot schemes, II

Indranil Biswas and Harish Seshadri

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1441790384

Digital Object Identifier
doi:10.1215/ijm/1441790384

Mathematical Reviews number (MathSciNet)
MR3285865

Zentralblatt MATH identifier
1327.14036

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

Citation

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. https://projecteuclid.org/euclid.ijm/1441790384


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