Applications of Algebraic Geometry to Coding Theory, Physics and Computation

✍ Scribed by I. Burban, Yu. Drozd, G.-M Greuel (auth.), Ciro Ciliberto, Friedrich Hirzebruch, Rick Miranda, Mina Teicher (eds.)

• Publisher: Springer Netherlands
• Year: 2001
• Tongue: English
• Leaves: 343
• Series: NATO Science Series 36 Series II
• Edition: 1
• Category: Library

✦ Synopsis

An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision. Contributions on more fundamental aspects of algebraic geometry include expositions related to counting points on varieties over finite fields, Mori theory, linear systems, Abelian varieties, vector bundles on singular curves, degenerations of surfaces, and mirror symmetry of Calabi-Yau manifolds.

✦ Table of Contents

Front Matter....Pages I-XV
Vector Bundles on Singular Projective Curves....Pages 1-15
On Double Planes with Kodaira Dimension Zero....Pages 17-22
Computing Minimal Generators of Ideals of Elliptic Curves....Pages 23-35
The Segre and Harbourne-Hirschowitz Conjectures....Pages 37-51
Pillow Degenerations of K3 Surfaces....Pages 53-63
Computational Algebraic Geometry Today....Pages 65-119
Some Applications of Algebraic Curves to Computational Vision....Pages 121-137
Coding Theory and Algebraic Curves Over Finite Fields....Pages 139-159
Three Algorithms in Algebraic Geometry, Coding Theory and Singularity Theory....Pages 161-194
Counting Points on Calabi-Yau Threefolds....Pages 195-205
Subvarieties of Abelian Varieties....Pages 207-214
Characteristic Varieties of Algebraic Curves....Pages 215-254
Communication Networks and Hilbert Modular Forms....Pages 255-270
Compact Kähler Threefolds with Small Picard Numbers....Pages 271-290
Abelian Varieties over the Field of the 20th Roots of Unity That Have Good Reduction Everywhere....Pages 291-296
Using Monodromy to Decompose Solution Sets of Polynomial Systems into Irreducible Components....Pages 297-315
Diffeomorphisms and Families of Fourier-Mukai Transforms in Mirror Symmetry....Pages 317-337

✦ Subjects

Algebraic Geometry; Numeric Computing; Discrete Mathematics in Computer Science