An embedding of varieties is a way of placing one algebraic variety into another in such a manner that the first variety retains its structure within the second. This is done by associating points in the first variety to points in the second variety via a morphism that is both injective and respects the algebraic structure, often allowing for a clearer understanding of geometric properties and relationships. This concept is crucial when examining how different varieties relate to one another and interact through their coordinate rings.
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