Syllabus Math 511


Math 511. Intro to Algebraic Geometry Lecture Syllabus

The course will prepare students for research in algebraic geometry and related areas including number theory, algebraic combinatorics, logic, and complex geometry.

Topics include:

  • Plane Algebraic Curves
    • Smooth curves, local parameter
    • Function field of a curve
    • Rational curves
    • Bezout’s Theorem
  • Affine algebraic sets and varieties
  • Irreducible components
  • Regular and rational functions
  • Regular and rational maps
  • Projective and quasiprojective varieties
    • Projective spaces
    • Hypersurfaces and complete intersections
    • Grassmannians
  • Products of varieties
  • Normal varieties; normalization
  • Dimension
  • Singular and nonsingular points; tangent spaces
  • Birational maps; blowups
  • Divisors
    • Cartier and Weil divisors
    • Linear systems
    • Maps to projective space
  • The group law on a plane cubic

Possible texts:
Shafarevich, Basic Algebraic Geometry, Volume 1

Effective Spring 2014. (Approved by GAC, December 2012.)