Overview

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.

Full Product Details

Author:   Ciro Ciliberto ,  Friedrich Hirzebruch ,  Rick Miranda ,  Mina Teicher
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2001 ed.
Volume:   36
Dimensions:   Width: 17.00cm , Height: 2.00cm , Length: 24.40cm
Weight:   1.490kg
ISBN:  

9781402000041

ISBN 10:   1402000049
Pages:   337
Publication Date:   31 August 2001
Audience:   General/trade ,  College/higher education ,  General ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

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