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Algebraic Geometry II

Prof. Dr. Matthias Schütt
M.Sc.-Math. Roberto Laface

10:00 - 12:00

12:00 - 14:00

Exercise Sessions

14:00 - 16:00
Aim of the course

Continuing the study of algebraic varieties started in the course "Algebraic Geometry I", by introducing scheme theory and applications.

  • Lines on cubics surfaces
  • Schemes
  • Bezout's theorem
  • Divisors
  • Elliptic curves
  • Differentials
  • Riemann-Roch theorem for curves
  • Riemann-Hurwitz formula

Exercises & additional material


  • Commutative algebra:
  1. Atiyah, M. F.; Macdonald, I. G.: Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.
  2. Eisenbud, David: Commutative algebra with a view toward algebraic geometry. Graduate Texts in Mathematics, 150. Springer-Verlag, New York, 1995.
  • Algebraic Geometry:
  1. Hartshorne, Robin: Algebraic geometry. Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York-Heidelberg, 1977.
  2. Eisenbud, David; Harris, Joe: The geometry of schemes. Graduate Texts in Mathematics, 197. Springer-Verlag, New York, 2000.
  3. Hulek, Klaus: Elementary algebraic geometry. Translated from the 2000 German original by Helena Verrill. Student Mathematical Library, 20. American Mathematical Society, Providence, RI, 2003.
  4. Vakil, Ravi: Foundations of Algebraic Geometry. Notes of a course taught at Stanford, available at http://math.stanford.edu/~vakil/216blog/.