Lecture, three hours. Requisite: course 215A (or 210A, 210B, and 210C with consent of instructor). Affine and projective varieties. Irreducibility, dimension, singular and smooth points. Rational maps, curves, intersections in projective space. Schemes. Proper and finite morphisms. Coherent and quasi-coherent sheaves. Divisors, line bundles, ampleness. S/U or letter grading.