Prevarieties and Varieties

Definition ([Gathmathh-AG, Definition 5.1]): A prevariety is a ringed space \(X\) that has a finite open cover by affine varieties. The elements of \(\mathcal{O}_X(U)\) for an open subset \(U\subseteq X\) are called regular functions.

References

• [Gathmann-AG] Class Notes “Algebraic Geometry” (2021/22 version) by Gathmann.
• [Vakil-TRS] The Rising Sea: Foundations of Algebraic Geometry Notes (July 27, 2024 version) by Vakil.