On the curvature of symmetric products of a compact Riemann surface

2013/02/03 by Indranil Biswas, Biswas, Indranil
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Meromorphic and Entire Functions #math.DG #msc:14C20 #msc:32Q10

paper · pdf · doi:10.48550/arxiv.1302.0472

arxiv created 2013/02/03 · arxiv updated 2013/02/05

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 ≤ 2(\rm genus(X)-1), the symmetric product Sⁿ(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.

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