Applications of Algebraic Geometry to Coding Theory, Physics and Computation

By: Ciro Ciliberto (Editor), Friedrich Hirzebruch (Editor), Rick Miranda (Editor)

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Hardcover | 31 August 2001

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356 Pages

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23.5 x 16.51 x 2.54

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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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Preface	p. VII
List of participants	p. IX
List of contributors	p. XIII
Vector bundles on singular projective curves	p. 1
On double planes with Kodaira dimension zero	p. 17
Computing minimal generators of ideals of elliptic curves	p. 23
The Segre and Harbourne-Hirschowitz conjectures	p. 37
Pillow degenerations of K3 surfaces	p. 53
Computational algebraic geometry today	p. 65
Some applications of algebraic curves to computational vision	p. 121
Coding theory and algebraic curves over finite fields	p. 139
Three algorithms in algebraic geometry, coding theory and singularity theory	p. 161
Counting points on Calabi-Yau threefolds	p. 195
Subvarieties of abelian varieties	p. 207
Characteristic varieties of algebraic curves	p. 215
Communication networks and Hilbert modular forms	p. 255
Compact Kahler threefolds with small Picard numbers	p. 271
Abelian varieties over the field of the 20th roots of unity that have good reduction everywhere	p. 291
Using monodromy to decompose solution sets of polynomial systems into irreducible components	p. 297
Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry	p. 317
Table of Contents provided by Syndetics. All Rights Reserved.

Applications of Algebraic Geometry to Coding Theory, Physics and Computation

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Hardcover

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