On the Kähler structures over Quot schemes

2014/01/29 by Biswas, Indranil, Seshadri, Harish
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.7408

Abstract

Let Sⁿ(X) be the n-fold symmetric product of a compact connected Riemann surface X of genus g and gonality d. We prove that Sⁿ(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^{⊕ r}_X of degree n. If g ≥ 2 and n ≤ 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.

Related

• On the Kähler structures over Quot schemes, II
• On Kaehler structures over symmetric products of a Riemann surface
• Quot schemes and Ricci semipositivity
• On the curvature of symmetric products of a compact Riemann surface
• Compact Kähler manifolds with nonpositive bisectional curvature