Lecture
This lecture covers the definition of projective, quasi-projective, and algebraic varieties, explaining the differences between them. The instructor introduces the concept of morphisms between varieties, focusing on the ring of regular functions and its importance in defining morphisms. The lecture concludes with a detailed proof of the relation between affine and projective varieties, highlighting the isomorphisms between them and the finite open coverings by quasi-affine varieties. Additionally, the instructor presents a lemma simplifying the verification of morphisms when the target is an affine variety.