In the context of algebraic geometry and complex geometry, a **dual abelian variety** can be understood in terms of the theory of abelian varieties and their duals. An abelian variety is a complete algebraic variety that has a group structure, and duality is an important concept in this theory.
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The dual of an abelian variety represents algebraically trivial line bundles rigidified at the origin. Its group law is tensor product. A group homomorphism induces by pullback of these line bundles.