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arithmetic genus
In mathematics, the arithmetic genus of an algebraic variety is one of a few possible generalizations of the genus of an algebraic curve or Riemann surface.
==Complex projective manifolds==
The arithmetic genus of a complex projective manifold
of dimension ''n'' can be defined as a combination of Hodge numbers, namely
:''p''''a'' = ''h''''n'',0 − ''h''''n'' − 1, 0 + ... + (−1)''n'' − 1''h''1, 0.
When ''n'' = 1 we have χ = 1 − ''g'' where ''g'' is the usual (topological) meaning of genus of a surface, so the definitions are compatible.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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