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In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4. More specifically there are two closely related types of quartic surface: affine and projective. An ''affine'' quartic surface is the solution set of an equation of the form : where ''f'' is a polynomial of degree 4, such as ''f''(''x'',''y'',''z'') = ''x''4 + ''y''4 + ''xyz'' + ''z''2 − 1. This is a surface in affine space A3. On the other hand, a projective quartic surface is a surface in projective space P3 of the same form, but now ''f'' is a ''homogeneous'' polynomial of 4 variables of degree 4, so for example ''f''(''x'',''y'',''z'',''w'') = ''x''4 + ''y''4 + ''xyzw'' + ''z''2''w''2 − ''w''4. If the base field in R or C the surface is said to be ''real'' or ''complex''. One must be careful to distinguish between algebraic Riemann surfaces, which are in fact quartic curves over C, and quartic surfaces over R. For instance, the Klein quartic is a ''real'' surface given as a quartic curve over C. If on the other hand the base field is finite, then it is said to be an ''arithmetic quartic surface''. ==Special quartic surfaces== * Dupin cyclides * The Fermat quartic, given by ''x''4 + ''y''4 + ''z''4 + ''w''4 =0 (an example of a K3 surface). * More generally, certain K3 surfaces are examples of quartic surfaces. * Kummer surface * Plücker surface * Weddle surface 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「quartic surface」の詳細全文を読む スポンサード リンク
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