Math 6422: Algebraic Geometry II

Instructor: Anton Leykin
  • Contact:
  • Skiles 109
  • Office hours: Mon 4pm, Tue/Thu 2pm, or by appointment
When and where:

1:05 pm - 1:55 pm, MWF, Skiles 169


This course is an introduction to the subject from a computational angle. The main focus will be on concrete construction of affine and projective varieties, constructive proofs of basic theorems, and theory behind the algorithms used to manipulate various algebro-geometric objects. Two computational gadgets will play a prominent role: Groebner bases (a symbolic exact technique) and polynomial homotopy continuation (a numerical approximate technique).

  • Parts of Cox, Little, O'Shea, ``Using algebraic geometry'' (e-text available for free from the library)
  • Instructor's notes
Student activities:
  • Homework: problem sets (exercises from the textbook) assigned every two weeks.
  • In-class exercises: problems solved and discussed in class in small groups.
  • There will be no exams.
  • Free software: Macaulay2 (recommended), CoCoA, Singular, Sage.
  • Commercial software: Mathematica, Maple.