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In mathematics, a Beauville surface is one of the surfaces of general type introduced by . They are examples of "fake quadrics", with the same Betti numbers as quadric surfaces. ==Construction== Let ''C''1 and ''C''2 be smooth curves with genera ''g''1 and ''g''2. Let ''G'' be a finite group acting on ''C''1 and ''C''2 such that *''G'' has order (''g''1 − 1)(''g''2 − 1) *No nontrival element of ''G'' has a fixed point on both ''C''1 and ''C''2 *''C''1/''G'' and ''C''2/''G'' are both rational. Then the quotient (''C''1 × ''C''2)/''G'' is a Beauville surface. One example is to take ''C''1 and ''C''2 both copies of the genus 6 quintic ''X''5 + ''Y''5 + ''Z''5 =0, and ''G'' to be an elementary abelian group of order 25, with suitable actions on the two curves. 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「Beauville surface」の詳細全文を読む スポンサード リンク
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