Chern scalar curvature and symmetric products of compact Riemann surfaces

2018/04/12 by Biswas, Indranil, Seshadri, Harish
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.04524

Abstract

Let X be a compact connected Riemann surface of genus g≥ 0, and let \rm Sym^d(X), d ≥ 1, denote the d-fold symmetric product of X. We show that \rm Sym^d(X) admits a Hermitian metric with negative Chern scalar curvature if and only if g ≥ 2, and positive Chern scalar curvature if and only if d > g.

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