Algebraic Geometry
MIT OpenCourseWare presents the first semester of a two-semester graduate sequence on algebraic geometry. The course introduces algebraic varieties over an algebraically closed field, examines the relationship between complex algebraic varieties and complex analytic varieties, and works through examples emphasizing algebraic curves and surfaces. It builds toward the language of schemes and the properties of morphisms between them, the framework underlying modern algebraic geometry. Materials include lecture notes, problem sets, and a syllabus covering the semester's topics in sequence. No enrollment or certificate is offered; the course is provided freely as MIT OpenCourseWare material for self-study, aimed at graduate students or advanced undergraduates with a solid background in commutative algebra. It sets up the technical foundation needed for the second semester's deeper treatment of scheme theory and cohomology.