On the curvature of symmetric products of a compact Riemann surface |
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Authors: | Indranil Biswas |
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Institution: | 1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400005, India
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Abstract: | Let X be a compact connected Riemann surface of genus at least two. The main theorem of Bökstedt and Romão 3] says that for any positive integer n ≤ 2(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. |
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