Algebraic Geometry
MIT OpenCourseWare's graduate course covers the foundations of algebraic varieties defined over an algebraically closed field, including affine and projective varieties, morphisms, dimension theory, and singularities. It develops the correspondence between complex algebraic varieties and complex analytic varieties, showing where algebraic and analytic methods agree and where they diverge. Materials include lecture notes, problem sets, and a full syllabus tracing the course's progression from basic definitions through sheaf-theoretic tools used in modern algebraic geometry. The course assumes prior exposure to commutative algebra and abstract algebra and is aimed at advanced undergraduates or beginning graduate students. As with other MIT OCW offerings, all materials are free to access online with no enrollment or certificate, under a Creative Commons license, making it a self-study resource rather than an instructor-led class.