Topics in Algebraic Geometry: Intersection Theory on Moduli Spaces
This MIT OCW graduate course covers intersection theory on moduli spaces, a topic that changes focus each semester it is taught. The syllabus works through the geometry of homogeneous varieties, then builds up to the Deligne-Mumford moduli spaces of stable curves and the Kontsevich moduli spaces of stable maps, using intersection theory as the main tool throughout. Materials follow MIT OpenCourseWare's standard format of lecture notes and problem sets drawn from the actual course as taught on campus. The subject sits at an advanced level, assuming prior graduate coursework in algebraic geometry, and it is aimed at students who already know schemes, sheaves, and cohomology and want to see how those tools apply to the specific, heavily studied objects that parametrize curves and maps. No certificate is offered; MIT OCW publishes the materials for self-study at no cost.