Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 763: Introduction to Algebraic Geometry

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.
  • Divisors.
  • Low-dimensional varieties: curves and surfaces. Blow-ups.
  • The Riemann-Roch Theorem.
Math 742 or equivalent

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, WI  53706

(608) 263-3054

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