Commutative Algebra, Singularities and Computer Algebra : Proceedings of the NATO Advanced Research Workshop on Commutative Algebra, Singularities and Computer Algebra Sinaia, Romania 17–22 September 2002

**Commutative Algebra, Singularities and Computer Algebra** presents current trends in commutative algebra, algebraic combinatorics, singularity theory and computer algebra, and highlights the interaction between these disciplines. Contributions by leading international mathematicians thoroughly discuss topics in: modules theory, integrally closed ideals and determinantal ideals, singularities in projective spaces and Castelnuovo-Mumford regularity, Groebner and SAGBI basis, and the use of the computer packages Bergman, CoCoA and SINGULAR. Front Matter....Pages i-x Association for Flag Configurations....Pages 1-8 Gröbner Bases and Determinantal Ideals....Pages 9-66 Bounds for Castelnuovo-Mumford Regularity in Terms of Degrees of Defining Equations....Pages 67-73 The Computer Algebra Package Bergman: Current State....Pages 75-100 Monomialization and Ramification of Valuations....Pages 101-111 Hyperplane Arrangements, M-Tame Polynomials and Twisted Cohomology....Pages 113-126 A Note on the Intersection of Veronese Surfaces....Pages 127-139 Rank One Maximal Cohen-Macaulay Modules Over Singularities of Type Y 1 3 + Y 2 3 + Y 3 3 + Y 4 3 ....Pages 141-157 Towards a Theory of Gorenstein....Pages 159-177 Universal Gröbner Bases, Integer Programming and Finite Graphs....Pages 179-190 Torsion in Tensor Powers and Flatness....Pages 191-196 Basic Tools for Computing in Multigraded Rings....Pages 197-216 A Problem in Group Theory Solved by Computer Algebra....Pages 217-223 On Curves of Small Degree on a Normal Rational Surface Scroll....Pages 225-239 On Sagbi Bases and Resultants....Pages 241-254 Modules of G-Dimension Zero over Local Rings with the Cube of Maximal Ideal Being Zero....Pages 255-273 The notion of association, as used for example by Castelnuovo or Coble [2], expresses the fact that the projective invariants of configurations of n ordered points in PD-1 can be identified with the projective invariants of associated configurations of n points in Pn-D-1. Proceedings of the NATO Advanced Research Workshop, held in Sinaia, Romania, 17-22 September 2002