Applications of Algebraic Geometry to Coding Theory, Physics and Computation

ISBN-13: 9781402000058 / Angielski / Miękka / 2001 / 337 str.

Ciro Ciliberto; Friedrich Hirzebruch; Rick Miranda

Opis

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.

Spis treści

Preface. List of Participants. List of contributors. Vector bundles on singular projective curves; I. Burban, et al. On double planes with Kodaira dimension zero; A. Calabri. Computing minimal generators of ideals of elliptic curves; L. Chiantini, et al. The Segre and Harbourne-Hirschowitz conjectures; C. Ciliberto, R. Miranda. Pillow degenerations of K3 surfaces; C. Ciliberto, et al. Computational algebraic geometry today; W. Decker, F.-O. Schreyer. Some applications of algebraic curves to computational vision; M. Fryers, et al. Coding theory and algebraic curves over finite felds; G. van der Geer. Three algorithms in algebraic geometry, coding theory and singularity theory; G.-M. Greuel, et al. Counting points on Calabi-Yau threefolds; K. Hulek, J. Spandaw. Subvarieties of abelian varieties; E. Izadi. Characteristic varieties of algebraic curves; A. Libgober. Communications networks and Hilbert modular forms; R. Livné. Compact Kähler threefolds with small Picard numbers; Th. Peternell. Abelian varieties over the field of the 20th roots of unity that have good reduction everywhere; R. Schoof. Using monodromy to decompose solution sets of polynomial systems into irreducible components; A.J. Sommese, et al. Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry; B. Szendroi.