Talk:Arithmetic genus

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WikiProject Mathematics (Rated Start-class, Mid-importance)
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Mathematics rating:
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 Field:  Geometry

Some mathematical correction was necessary: First, h^{p,q} is equal to h^{q,p} only for projective and other Kaehler compact complex manifolds, but not for arbitrary compact complex manifolds. Moreover, the definition can not be used for arbitrary non-compact complex manifolds or arbitrary locally ringed spaces, because the alternating sum does not make any sense if some of the terms are infinite. So some compactness assumption is necesssary, in order to ensure that the hodge numbers resp. cohomology group dimensions are finite.

Joerg Winkelmann (talk) 02:12, 28 January 2010 (UTC)