Oberwolfach Seminar: Computational Algebraic Geometry

November 16th - 22nd, 2003
Deadline for applications:
October 15, 2003
Christoph Lossen, Kaiserslautern
Frank Schreyer, Saarbrücken
Frank Sottile, University of Massachussets
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.
Basic knowledge in algebraic geometry.
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