Applications of Algebraic Geometry to Coding Theory, Physics and Computation

by Ciliberto, Ciro; Hirzebruch, Friedrich; Miranda, Rick; Teicher, Mina

• ISBN13: 9781402000058
• ISBN10: 1402000057
• Format: Paperback
• Copyright: 2001-10-01
• Publisher: Kluwer Academic Pub

Summary

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

Preface	vii
List of participants	ix
List of contributors	xiii
Vector bundles on singular projective curves	1	(16)
I. Burban
Yu. Drozd
G -M. Greuel
On double planes with Kodaira dimension zero	17	(6)
A. Calabri
Computing minimal generators of ideals of elliptic curves	23	(14)
L. Chiantini
F. Cioffi
F. Orecchia
The Segre and Harbourne-Hirschowitz conjectures	37	(16)
C. Ciliberto
R. Miranda
Pillow degenerations of K3 surfaces	53	(12)
C. Ciliberto
R. Miranda
M. Teicher
Computational algebraic geometry today	65	(56)
W. Decker
F.-O. Schreyer
Some applications of algebraic curves to computational vision	121	(18)
M. Fryers
J. Y. Kaminski
M. Teicher
Coding theory and algebraic curves over finite fields	139	(22)
G. van der Geer
Three algorithms in algebraic geometry, coding theory and singularity theory	161	(34)
G. -M. Greuel
C. Lossen
M. Schulze
Counting points on Calabi-Yau threefolds	195	(12)
K. Hulek
J. Spandaw
Subvarieties of abelian varieties	207	(8)
E. Izadi
Characteristic varieties of algebraic curves	215	(40)
A. Libgober
Communication networks and Hilbert modular forms	255	(16)
R. Livne
Compact Kuhler threefolds with small Picard numbers	271	(20)
Th. Peternell
Abelian varieties over the field of the 20th roots of unity that have good reduction everywhere	291	(6)
R. Schoof
Using monodromy to decompose solution sets of polynomial systems into irreducible components	297	(20)
A. J. Sommese
J. Verschelde
C. W. Wampler
Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry	317
B. Szendroi