Alexander Pavlov (Fall 2017):
Andrei Caldararu, Fall 2016:
This is a first course in algebraic geometry. While there are no formal prerequisites beyond a knowledge of the material covered in the first-year algebra and geometry sequence, familiarity with some basic commutative algebra will be helpful. I will follow roughly the first chapter of Hartshorne's book, but at some point we'll move on to the study of divisors, linear equivalence, Riemann-Roch, and related topics.
Topics covered will include:
- Affine and projective varieties.
- Morphisms and rational maps.
- Local properties: smoothness and dimension. Tangent space.
- Degree of projective varieties and Bezout's Theorem.
- Low-dimensional varieties: curves and surfaces. Blow-ups.
- The Riemann-Roch Theorem.