MA 308: Basic Algebraic Geometry
Credits: 3:0
Prerequisite courses: Algebra II (MA 213).
Pre-requisites :
- The course will assume that that the student is comfortable with Abstract Algebra at the level of Galois theory.
- We will develop all the Commutative algebra that we will need.
The material to be covered will include:
- Affine algebraic sets: Zariski topology, irreducible components, Hilbert Nullstellensatz theorem, maps of algebraic sets
- Algebraic varieties: Definitions, affine algebraic varieties, projective varieties, morphisms
- Rational functions and rational maps
- Algebraic curves, B´ezout’s theorem * Reimann-Roch theorem
Suggested books and references:
- William D. Fulton, Algebraic curves, available free (and legally) at http://www.math.lsa.umich.edu/ wfulton/CurveBook.pdf.