Math 763 -- Algebraic Geometry I

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Fall 2019

Homework assignments

Course description

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. The rough outline of the course is as follows (subject to change):

  • Affine and projective varieties.
  • Morphisms and rational maps.
  • Local properties: smoothness and dimension. Tangent space.
  • Divisors.
  • Low-dimensional varieties: curves and surfaces. Blow-ups.
  • The Riemann-Roch Theorem.

Here is a more detailed lecture-by-lecture list of topics that I covered in the past, of course, this is all subject to change.


References

  • Shafarevich, Basic Algebraic Geometry.
  • Algebraic Geometry (online notes) by Milne.
  • Hartshorne, Algebraic Geometry, Chapter I (this is more advanced, so does not quite match the content).
  • Here is a discussion on MathOverflow with more books on algebraic geometry, but most of them are going to be too advanced.

Information for students

  • Instructor: Dima Arinkin
  • Office Hours: Tuesday 3-4pm, Wednesday 2-2:45pm, and by appointment in VV 603
  • Lectures: TuTh 11am-12:15pm, VV B129
  • Grade: There will be weekly homework assignments, but no exams in this course.