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In algebraic geometry, a hyperelliptic curve is an algebraic curve given by an equation of the form : where ''f(x)'' is a polynomial of degree ''n'' > 4 with ''n'' distinct roots. A hyperelliptic function is an element of the function field of such a curve or possibly of the Jacobian variety on the curve, these two concepts being the same in the elliptic function case, but different in the present case. Fig. 1 is the graph of where : ==Genus of the curve== The degree of the polynomial determines the genus of the curve: a polynomial of degree 2''g'' + 1 or 2''g'' + 2 gives a curve of genus ''g''. When the degree is equal to 2''g'' + 1, the curve is called an imaginary hyperelliptic curve. Meanwhile, a curve of degree 2''g'' + 2 is termed a real hyperelliptic curve. This statement about genus remains true for ''g'' = 0 or 1, but those curves are not called "hyperelliptic". Rather, the case ''g'' = 1 (if we choose a distinguished point) is an elliptic curve. Hence the terminology. 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「Hyperelliptic curve」の詳細全文を読む スポンサード リンク
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