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In mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes. For each of these classes, the surfaces in the class can be parametrized by a moduli space. For most of the classes the moduli spaces are well understood, but for the class of surfaces of general type the moduli spaces seem too complicated to describe explicitly, though some components are known. described the classification of complex projective surfaces. later extended the classification to include non-algebraic compact surfaces. The analogous classification of surfaces in characteristic ''p'' > 0 was begun by and completed by ; it is similar to the characteristic 0 projective case, except that one also gets singular and supersingular Enriques surfaces in characteristic 2, and quasi hyperelliptic surfaces in characteristics 2 and 3. ==Statement of the classification== The Enriques–Kodaira classification of compact complex surfaces states that every nonsingular minimal compact complex surface is of exactly one of the 10 types listed on this page; in other words, it is one of the rational, ruled (genus >0), type VII, K3, Enriques, Kodaira, toric, hyperelliptic, properly quasi-elliptic, or general type surfaces. For the 9 classes of surfaces other than general type, there is a fairly complete description of what all the surfaces look like (which for class VII depends on the global spherical shell conjecture, still unproved in 2009). For surfaces of general type not much is known about their explicit classification, though many examples have been found. The classification of algebraic surfaces in positive characteristics (, ) is similar to that of algebraic surfaces in characteristic 0, except that there are no Kodaira surfaces or surfaces of type VII, and there are some extra families of Enriques surfaces in characteristic 2, and hyperelliptic surfaces in characteristics 2 and 3, and in Kodaira dimension 1 in characteristics 2 and 3 one also allows quasielliptic fibrations. These extra families can be understood as follows: In characteristic 0 these surfaces are the quotients of surfaces by finite groups, but in finite characteristics it is also possible to take quotients by finite group schemes that are not étale. Oscar Zariski constructed some surfaces in positive characteristic that are unirational but not rational, derived from inseparable extensions (Zariski surfaces). Serre showed that ''h''0(Ω) may differ from ''h''1(''O''). Igusa showed that even when they are equal, they may be greater than the irregularity defined as the dimension of the Picard variety. 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「Enriques–Kodaira classification」の詳細全文を読む スポンサード リンク
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