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Vanishing first betti number of kaehler manifold with global SU(m) holonomy

by Ygor
Tags: holonomy, kaehler
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Ygor
#1
Jul2-09, 07:36 AM
P: 4
Hi,

I have the following question. In "Joyce D.D. Compact manifolds with special holonomy" I read on page 125 that a compact Kaehler manifold with global holonomy group equal to SU(m), has vanishing first betti number, or more specifically vanishing Hodge numbers h^(1,0)= h^(0,1) = 0. However, in "Candelas, Lectures on complex manifolds" the constrains h^1 = 0 is not automatic if the holonomy equals SU(m).

So, I wonder, which case is the correct one?

I hope anyone could help me out,

Ygor
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