**Date:**- November 16th - 22nd, 2003
**Deadline for applications:**- October 15, 2003
**Organizers:**- Christoph Lossen, Kaiserslautern
- Frank Schreyer, Saarbrücken
- Frank Sottile, University of Massachussets
**Subjects:**- Algebraic geometry got computational accessible through the theory of Gröbner basis. The course starts with Gröbner basics: ideal membership, normal forms, syzygies, intersections, elimination, projective closure, Hilbert function, dimension, degree, tangent cone, intersection multiplicities, and proceeds with more advanced topics: normalization, rational parameterization of curves (and surfaces) cohomology of coherent sheaves, Tate resolutions, monads, resultants, versal deformations of singularities and modules, special families (existence, uni-rationality), enumerative geometry, real solutions, D-modules, monodromy.
**Prerequisites:**- Basic knowledge in algebraic geometry.
**Literature:**-
Greuel, Gert-Martin; Pfister, Gerhard
*A singular introduction to commutative algebra. With contributions by Olaf Bachmann, Christoph Lossen and Hans Schönemann.*Berlin: Springer (2002).Cox, David; Little, John; O'Shea, Donal

*Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra.*2nd ed. Undergraduate Texts in Mathematics. New York: Springer (1996).Hartshorne, Robin

*Algebraic geometry.*Corr. 3rd printing. Graduate Texts in Mathematics, 52. New York-Heidelberg-Berlin: Springer (1983).

Mathematisches Forschungsinstitut Oberwolfach updated: August 15th, 2003