On the curvature of symmetric products of a compact Riemann surface

Abstract

Let $X$ be a compact connected Riemann surface of genus at least two. The main theorem of arxiv:1010.1488 says that for any positive integer $n\le 2(\mathrm{genus}(X)-1)$, the symmetric product $S^n(X)$ does not admit any Kähler metric satisfying the condition that all the holomorphic bisectional curvatures are nonnegative. Our aim here is to give a very simple and direct proof of this result of Bökstedt and Romão.

References in corpus (1)

• On the curvature of vortex moduli spaces