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Topics of this course are
- Hilbert's Nullstellensatz and Gröbner basis
- The algebra-geometry dictionary
- Noetherian rings and primary decomposition
- Localization
- Rational functions and dimension
- Integral ring extension and Krull dimension
- Constructive ideal and module theory
- Projective algebraic geometry
- Bézous's theorem
- Local rings and power series
- Products and morphism of projective varieties
- Resolution of curve singularities
- Families of varieties
- Bertini's theorem and applications
- The geometric genus of a plane curve
| D. Cox, J. Little and D. O'Shea | Ideals, Varieties, and Algorithm, 4-th addition | Springer, UTM | 2005 |
| W. Fulton | Algebraic curves |
Benjamin |
1969 |
| M. Kreuzer and L. Robbiano | Computational Commutative Algebra 1 | Springer | 2000 |
| B.L. van de Waerden | Moderne Algebra | Springer, GL 33-34 | 1937 |
| D. Eisenbud | Commutative Algebra with a View Towards Algebraic Geometry | Springer, GTM 150 | 1995 |
| M.F. Atiyah and I.G Macdonald | Introduction to Commutative Algebra | Addison-Wesley |
1969 |
- 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
Regular attendance to exercise sessions. Oral exam at the end of term.
| Frank-Olaf Schreyer Zi. 429, Geb. E2 4 D-66123 Saarbrücken Tel. +49(0)681/302-2785 This email address is being protected from spambots. You need JavaScript enabled to view it. |