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Winter 2013 On the Kähler structures over Quot schemes
Indranil Biswas, Harish Seshadri
Illinois J. Math. 57(4): 1019-1024 (Winter 2013). DOI: 10.1215/ijm/1417442560

Abstract

Let $S^{n}(X)$ be the $n$-fold symmetric product of a compact connected Riemann surface $X$ of genus $g$ and gonality $d$. We prove that $S^{n}(X)$ admits a Kähler structure such that all the holomorphic bisectional curvatures are nonpositive if and only if $n<d$. Let $\mathcal{Q}_{X}(r,n)$ be the Quot scheme parametrizing the torsion quotients of $\mathcal{O}^{\oplus r}_{X}$ of degree $n$. If $g\geq 2$ and $n\leq 2g-2$, we prove that $\mathcal{Q}_{X}(r,n)$ does not admit a Kähler structure such that all the holomorphic bisectional curvatures are nonnegative.

Citation

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Indranil Biswas. Harish Seshadri. "On the Kähler structures over Quot schemes." Illinois J. Math. 57 (4) 1019 - 1024, Winter 2013. https://doi.org/10.1215/ijm/1417442560

Information

Published: Winter 2013
First available in Project Euclid: 1 December 2014

zbMATH: 1304.14012
MathSciNet: MR3285865
Digital Object Identifier: 10.1215/ijm/1417442560

Subjects:
Primary: 14C20, 32Q05, 32Q10

Rights: Copyright © 2013 University of Illinois at Urbana-Champaign

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Vol.57 • No. 4 • Winter 2013
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