Jump to content

Talk:Arithmetic genus

Page contents not supported in other languages.
From Wikipedia, the free encyclopedia
This article is rated Start-class on Wikipedia's content assessment scale.
It is of interest to the following WikiProjects:
Mathematics Mid-priority
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
MidThis article has been rated as Mid-priority on the project's priority scale.

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)[reply]