Since we didn't cover quite enough of Part I during the Fall Quarter, we'll have to do a few topics from Part I of the text before proceeding to Part II. Here is our tentative list of topics. We'll study as many of them as we can in the time that is available.

• The Nullstellensatz; consequences and applications (Lecture 5 in the text)
• Further examples:
  • Families of Varieties (Lecture 4 in the text)
  • Grassmannians (Lecture 5 in the text)
• Dimension (and some specific examples) (Lectures 11 and 12 in the text)
• Hilbert polynomials (Lecture 14 in the text)
• Smoothness and tangent spaces (Lecture 15 in the text)
• Degree (and some specific examples) (Lectures 18 and 19 in the text)
• Singular points and tangent cones (Lecture 21 in the text)

As in Math 8203, the required work in the course will consist of solving exercises from the text and writing up the solutions.

Joel Roberts
351 Vincent Hall
625-1076
e-mail: roberts@math.umn.edu
http://www.math.umn.edu/~roberts