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In mathematics, an abelian surface is 2-dimensional abelian variety. One-dimensional complex tori are just elliptic curves and are all algebraic, but Riemann discovered that most complex tori of dimension 2 are not algebraic. The algebraic ones are called abelian surfaces and are exactly the 2-dimensional abelian varieties. Most of their theory is a special case of the theory of higher-dimensional tori or abelian varieties. Criteria to be a product of two elliptic curves (up to isogeny) were a popular study in the nineteenth century. Invariants: The plurigenera are all 1. The surface is diffeomorphic to ''S''1×''S''1×''S''1×''S''1 so the fundamental group is Z4. Hodge diamond: Examples: A product of two elliptic curves. The Jacobian variety of a genus 2 curve. ==See also== * Hodge theory 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「abelian surface」の詳細全文を読む スポンサード リンク
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