Math 662: Algebraic Geometry

Instructor: Frank Sottile
Lectures: TuTh 9:35--10:50 Milner 313
Course webpage: www.math.tamu.edu/~sottile/teaching/10.1/AG.html
Grading: Based on regular homework and class participation.
Schedule
  • Affine algebraic sets
    • Ideals and affine varieties
    • Irreducibility
    • Nullstellensatz
    • First step towards Bézout's Theorem
  • Projective algebraic sets
    • Projective spaces
    • Ideal of a projective algebraic set
  • Sheaves and varieties
    • Structural sheaf of an affine algebraic set
    • Algebraic varieties
    • Local rings
    • Sheaves of modules on affine and projective varieties
  • Dimension
    • Topological definition and the link with algebra
    • Dimension and counting equations
    • Morphisms and dimension
  • Tangent spaces and singular points
    • Singular points
    • Regular local rings
    • Curves
  • Bézout's Theorem
    • Intersection multiplicities
    • Bézout's Theorem
  • Sheaf cohomology
  • Arithmetic genus of curves and the weak Riemann-Roch theorem
    • Euler-Poincaré characteristic
    • Degree and genus of projective curves, Riemann-Roch 1
    • Divisors on a curve and Riemann-Roch 2
  
Last modified: Thur Oct 15 03:06:42 CST 2009