On Kaehler structures over symmetric products of a Riemann surface

2011/06/19 by Biswas, Indranil
#14C20 #32Q05 #32Q10 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1106.3733

Abstract

Given a positive integer n and a compact connected Riemann surface X, we prove that the symmetric product Sⁿ(X) admits a Kaehler form of nonnegative holomorphic bisectional curvature if and only if genus(X) ≤ 1. If n is greater than or equal to the gonality of X, we prove that Sⁿ(X) does not admit any Kaehler form of nonpositive holomorphic sectional curvature.

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