Topics in Algebraic Geometry: Algebraic Surfaces
This MIT graduate seminar works through the classification of algebraic surfaces, covering the Enriques-Castelnuovo classification in characteristic zero and the Bombieri-Mumford extension to characteristic p. Sessions build up the theory through worked examples, treating both the geometry and arithmetic of surfaces as far as the material allows. The course assumes solid grounding in algebraic geometry and is aimed at students already familiar with schemes and cohomological methods. Materials are provided through MIT OpenCourseWare, including lecture notes and reading references, free to access without enrollment or certificate. It suits students or independent learners wanting a rigorous treatment of surface classification theory rather than an introductory survey.