Applications of Algebraic Geometry to Coding Theory, Physics and Computation
Published on 6. December 2012
XV, 337 pages
978-94-010-1011-5 (ISBN)
Description
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.
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Other editions
Additional editions
Ciro Ciliberto | Friedrich Hirzebruch | Rick Miranda
Applications of Algebraic Geometry to Coding Theory, Physics and Computation
Proceedings of the NATO Advanced Research Workshop, held in Eilat, Israel, from 25th February to 1st March 2001
Book
08/2001
Kluwer Academic Publishers
€106.99
Shipment within 15-20 days
Content
Vector bundles on singular projective curves.- On double planes with Kodaira dimension zero.- Computing minimal generators of ideals of elliptic curves.- The Segre and Harbourne-Hirschowitz conjectures.- Pillow degenerations of K3 surfaces.- Computational algebraic geometry today.- Some applications of algebraic curves to computational vision.- Coding theory and algebraic curves over finite fields.- Three algorithms in algebraic geometry, coding theory and singularity theory.- Counting points on Calabi-Yau threefolds.- Subvarieties of abelian varieties.- Characteristic varieties of algebraic curves.- Communication networks and Hilbert modular forms.- Compact Kähler threefolds with small Picard numbers.- Abelian varieties over the field of the 20th roots of unity that have good reduction everywhere.- Using monodromy to decompose solution sets of polynomial systems into irreducible components.- Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry.
