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Applications of Algebraic Geometry to Coding Theory, Physics and Computation

  • Book
  • © 2001

Overview

Editors:
  1. Ciro Ciliberto

    1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Roma, Italy

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  2. Friedrich Hirzebruch

    1. Max Planck Institut für Mathematik, Bonn, Germany

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    You can also search for this editor in PubMed   Google Scholar

  3. Rick Miranda

    1. Department of Mathematics, Colorado State University, Fort Collins, USA

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  4. Mina Teicher

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

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Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry (NAII, volume 36)

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Table of contents (17 chapters)

  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
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Keywords

About this book

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.

Editors and Affiliations

  • 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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