MA 308: Basic Algebraic Geometry

Credits: 3:0

Prerequisite courses: Algebra II (MA 213).

Pre-requisites :

1. The course will assume that that the student is comfortable with Abstract Algebra at the level of Galois theory.
2. 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:

1. William D. Fulton, Algebraic curves, available free (and legally) at http://www.math.lsa.umich.edu/ wfulton/CurveBook.pdf.

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