## Illinois Journal of Mathematics

### On the Kähler structures over Quot schemes, II

#### 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
Revised: 24 March 2015
First available in Project Euclid: 9 September 2015

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

Digital Object Identifier
doi:10.1215/ijm/1441790384

Mathematical Reviews number (MathSciNet)
MR3285865

Zentralblatt MATH identifier
1327.14036

#### 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

#### References

• J. M. Baptista, On the $L^2$-metric of vortex moduli spaces, Nuclear Phys. B 844 (2011), 308–333.
• E. Bifet, F. Ghione and M. Letizia, On the Abel–Jacobi map for divisors of higher rank on a curve, Math. Ann. 299 (1994), 641–672.
• I. Biswas, A. Dhillon and J. Hurtubise, Automorphisms of the Quot schemes associated to compact Riemann surfaces, Int. Math. Res. Not. 2015 (2015), 1445–1460.
• I. Biswas and N. M. Romão, Moduli of vortices and Grassmann manifolds, Comm. Math. Phys. 320 (2013), 1–20.
• I. Biswas and H. Seshadri, On the Kähler structures over Quot schemes, Illinois J. Math. 57 (2013), 1019–1024.
• M. Bökstedt and N. M. Romão, On the curvature of vortex moduli spaces, Math. Z. 277 (2014), 549–573.
• N. Mok, The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature, J. Differential Geom. 27 (1988), 179–214.