Ebook: 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.

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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.
Content:
Front Matter....Pages i-x
Association for Flag Configurations....Pages 1-8
Gr?bner 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 Gr?bner 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

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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.
Content:
Front Matter....Pages i-x
Association for Flag Configurations....Pages 1-8
Gr?bner 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 Gr?bner 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
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