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arXiv · 1106.3733

On Kaehler structures over symmetric products of a Riemann surface

Indranil Biswas
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Abstract

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

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Indranil Biswas. 2012-02-29. On Kaehler structures over symmetric products of a Riemann surface. https://arxiv.org/abs/1106.3733

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