Instructor: Chad Schoen
Prerequisites: Math 252 (Commutative Algebra) and Math 272 (Riemann Surfaces)
The course treats concepts which are essential to further work in algebraic geometry. To the extent that other areas of mathematics require understanding of basic algebraic geometry concepts, this course is important for students with a wide range of research interests. Most researchers in the following fields need to be familiar with the rudiments of algebraic geometry: number theory, algebra, algebraic groups, quadratic forms, singularities, complex analytic geometry, string theory. Many topologists and differential geometers find knowledge of algebraic geometry valuable in their work as well.
Research in algebraic geometry requires an understanding of algebraic varieties over non-algebraically-closed fields and, more generally, of schemes. Although these topics will not be treated in detail in this course, the material will serve as preparation for these concepts.