Code: 2-MPG-104/15

Grading: Homeworks, final exam

You need to complete at least 50% of the homeworks to be admitted to the final (oral) exam.

If you achieve at least 90% success in your homeworks, you do not need to pass the final exam and you will receive a grade of A.

Otherwise, the final grade is the average of your homework success and your performance in the oral exam.

Lectures (in Slovak only):

  1. Varieties and Ideals, correction
  2. Zariski Topology
  3. Coordinate Ring of a Variety, correction
  4. Gröbner Bases
  5. Resultants
  6. Real Roots of a Polynomial Equation

Extra meetings:

There will be extra lectures (to compensate for the Wednesdays with no lecture):

  • Tuesday 7 May at 13:10 in M120
  • Tuesday 14 May at 13:10 in M120
  • Monday 20 May at 9:50 in X - cancelled / cancelled!

Homeworks:

  • sk, en - due by 27 February
  • sk, en - due by 6 March
  • sk, en - due by 13 March, solution to 21
  • sk, en - due by 20 March
  • sk, en - can be submitted by 3 April
  • sk, en - due by 10 April
    In the lecture, we reached page 25; next week we will continue with section 2.3 "Pullback of a Regular Function"
  • sk, en - due by 17 April
  • sk, en - due by 24 April
  • sk, en - due by 15 May (also covers the lecture on 7 May)

grading scheme

Oral exam:

Additional exercises (not to be submitted, just to assist your study): sk, en
Topics for the oral exam: sk, en. You will randomly select two of them and will also receive some related exercises.
The exam takes place on Tuesdays in June: 4 June, 11 June, 18 June at 9:00

Sources:

Brendan Hassett: Algebraic Geometry, Cambridge University Press, 2007
David Cox, John Little, Donal O'Shea: Ideals, Varieties and Algorithms, Springer Verlag, 1996
Justin R. Smith: Introduction to Algebraic Geometry, Five Dimensions Press, 2014
Igor R. Shafarevich: Basic Algebraic Geometry 1, Springer Verlag, 2010
A. Gathmann: Class Notes „Algebraic Geometry”, online lecture notes, 2014
Basu, R. Pollack, M.-F. Roy: Algorithms in Real Algebraic Geometry, Springer, 2003