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In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity ''q'' = 0 and the canonical line bundle ''K'' is non-trivial but has trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex numbers) and are elliptic surfaces of genus 0. Over fields of characteristic not 2 they are quotients of K3 surfaces by a group of order 2 acting without fixed points and their theory is similar to that of algebraic K3 surfaces. Enriques surfaces were first studied in detail by , though some of the Reye congruences introduced earlier by are also examples of Enriques surfaces. Enriques surfaces can also be defined over other fields. Over fields of characteristic other than 2, showed that the theory is similar to that over the complex numbers. Over fields of characteristic 2 the definition is modified, and there are two new families, called singular and supersingular Enriques surfaces, described by . ==Invariants== The plurigenera ''P''''n'' are 1 if ''n'' is even and 0 if ''n'' is odd. The fundamental group has order 2. The second cohomology group H2(''X'', Z) is isomorphic to the sum of the unique even unimodular lattice II1,9 of dimension 10 and signature -8 and a group of order 2. Hodge diamond: Marked Enriques surfaces form a connected 10-dimensional family, which showed is rational. 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 surface」の詳細全文を読む スポンサード リンク
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