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In mathematics, a Riemann form in the theory of abelian varieties and modular forms, is the following data: * A lattice Λ in a complex vector space Cg. * An alternating bilinear form α from Λ to the integers satisfying the following Riemann bilinear relations: # the real linear extension αR:Cg × Cg→R of α satisfies αR(''iv'', ''iw'')=αR(''v'', ''w'') for all (''v'', ''w'') in Cg × Cg; # the associated hermitian form ''H''(''v'', ''w'')=αR(''iv'', ''w'') + ''i''αR(''v'', ''w'') is positive-definite. (The hermitian form written here is linear in the first variable.) Riemann forms are important because of the following: * The alternatization of the Chern class of any factor of automorphy is a Riemann form. * Conversely, given any Riemann form, we can construct a factor of automorphy such that the alternatization of its Chern class is the given Riemann form. ==References== * * * * * 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「Riemann form」の詳細全文を読む スポンサード リンク
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