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Arithmetic genus : ウィキペディア英語版 | 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)』 ■ウィキペディアで「Arithmetic genus」の詳細全文を読む
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