On the Kähler structures over Quot schemes, II

2015/03/30 by Biswas, Indranil, Seshadri, Harish
#14H60 #14H81 #32Q10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.08530

Abstract

Let X be a compact connected Riemann surface of genus g, with g ≥ 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^{⊕ 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.

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