Algebraic Geometry (engl. version)


  • The lecture takes place on Tuesday and Friday, 10.15-11.45h in the "Zeichensaal" (U.39 in building E2 5)


Hilberts Nullstellensatz, Noethernormalization and Gröbner bases, primary decomposition, Krull dimension , Going up and Going down theorems, local study of algebraic sets, smoothness and singular points, intersectionmultiplicity of curves, linear systems of plane curves, the projective space, AF+BG Theorem, Bezout's Theorem, subvarieties of the projective space, morphisms, hilbertpolynomial, Bertini's Theorem, rational maps, Cremona transformation, divisors and linear series, Riemann inequality, Riemann-Roch Theorem, differential forms, adjoint curves, Hurwitzformula, canonical curves


 W. Decker, F.-O. Schreyer Varieties, Groebner Bases, and Algebraic Curves Manuscript  2009
M. F. Atiyah, I. G. Macdonald  Introduction to Commutative Algebra  Addison-Wesley  1969
 D. A. Cox, J. B. Little, D. B. O'Shea  Ideals, Varieties, and Algorithms  Springer  2007
M. Reid Undergraduate Algebraic Geometry Cambridge University Press 1988

Further literature will be anounce in the lecture.

Lecture notes:

VL1, VL2, VL3, VL4, VL5, VL6, VL7, VL8, VL9, VL10, VL11, VL12, VL13, VL14, VL15, VL16, VL17, VL18, VL 19, VL20, VL21, VL22, VL23, VL24, VL25, VL26, VL27, VL28


  • 4 hours lectures, 2 hours excercise session
  • 9 Credit points
  • 60h hours total time for lectures
  • 30h hours total time for excercises
  • 180h hours total time for self-study


The lecture takes place on Tuesday and Friday, 10.15-11.45h in the "Zeichensaal" (U.39 in building E2 5)


There will be exercise sheets each week. In order to be allowed to attend the exam at the end of the term, you have to achieve 50% of the maximal points in the exercises. In addition, you have to actively participate in the exercise sessions.


Exercise sheets:

schedule for the exercise sessions will be discussed in the first lecture.

Contact us

Prof. Dr. Frank-Olaf Schreyer
Zi. 425, Geb. E2 4
D-66123 Saarbrücken
Tel. +49(0)681/302-2785
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© AG Schreyer