Oberwolfach Seminar: Computational Algebraic Geometry

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).