Applications of Algebraic Geometry to Coding Theory, Physics and Computation

1. Front Matter

   Pages I-XV

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2. Vector Bundles on Singular Projective Curves

   • I. Burban, Yu. Drozd, G.-M Greuel

   Pages 1-15

3. On Double Planes with Kodaira Dimension Zero

   • A. Calabri

   Pages 17-22

4. Computing Minimal Generators of Ideals of Elliptic Curves

   • L. Chiantini, F. Cioffi, F. Orecchia

   Pages 23-35

5. The Segre and Harbourne-Hirschowitz Conjectures

   • C. Ciliberto, R. Miranda

   Pages 37-51

6. Pillow Degenerations of K3 Surfaces

   • C. Ciliberto, R. Miranda, M. Teicher

   Pages 53-63

7. Computational Algebraic Geometry Today

   • W. Decker, F.-O. Schreyer

   Pages 65-119

8. Some Applications of Algebraic Curves to Computational Vision

   • M. Fryers, J. Y. Kaminski, M. Teicher

   Pages 121-137

9. Coding Theory and Algebraic Curves Over Finite Fields

   • G. Van Der Geer

   Pages 139-159

10. Three Algorithms in Algebraic Geometry, Coding Theory and Singularity Theory

    • G.-M. Greuel, C. Lossen, M. Schulze

    Pages 161-194

11. Counting Points on Calabi-Yau Threefolds

    • K. Hulek, J. Spandaw

    Pages 195-205

12. Subvarieties of Abelian Varieties

    • E. Izadi

    Pages 207-214

13. Characteristic Varieties of Algebraic Curves

    • A. Libgober

    Pages 215-254

14. Communication Networks and Hilbert Modular Forms

    • R. Livné

    Pages 255-270

15. Compact Kähler Threefolds with Small Picard Numbers

    • Th. Peternell

    Pages 271-290

16. Abelian Varieties over the Field of the 20th Roots of Unity That Have Good Reduction Everywhere

    • R. Schoof

    Pages 291-296

17. Using Monodromy to Decompose Solution Sets of Polynomial Systems into Irreducible Components

    • A. J. Sommese, J. Verschelde, C. W. Wampler

    Pages 297-315

18. Diffeomorphisms and Families of Fourier-Mukai Transforms in Mirror Symmetry

    • B. Szendrői

    Pages 317-337

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.

• algorithms
• coding theory
• communication
• computer
• finite field
• geometry
• networks
• sets
• singularity theory

• Dipartimento di Matematica, Università di Roma “Tor Vergata”, Roma, Italy

  Ciro Ciliberto

• Max Planck Institut für Mathematik, Bonn, Germany

  Friedrich Hirzebruch

• Department of Mathematics, Colorado State University, Fort Collins, USA

  Rick Miranda

• Department of Mathematics and Computer Science, Bar-Ilan University, Ramat Gan, Israel

  Mina Teicher

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