Softcover ISBN:  9781470442477 
Product Code:  CONM/724 
List Price:  $117.00 
MAA Member Price:  $105.30 
AMS Member Price:  $93.60 
Electronic ISBN:  9781470451530 
Product Code:  CONM/724.E 
List Price:  $117.00 
MAA Member Price:  $105.30 
AMS Member Price:  $93.60 

Book DetailsContemporary MathematicsVolume: 724; 2019; 344 ppMSC: Primary 11; 14;
This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more.
Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography.
This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.ReadershipGraduate students and research mathematicians interested in algebraic geometry, cryptography, and elliptic and hyperelliptic curves.

Table of Contents

Articles

Boris M. Bekker and Yuri G. Zarhin  Families of elliptic curves with rational torsion points of even order

Lubjana Beshaj and Scott Guest  The weighted moduli space of binary sextics

Timothy J. Ford  A family of nonnormal double planes associated to hyperelliptic curves

Shuichi Otake and Tony Shaska  On the discriminant of certain quadrinomials

Tim Dokchitser, Vladimir Dokchitser, Céline Maistret and Adam Morgan  Semistable types of hyperelliptic curves

Andrew R. Stout  Formal deformations of algebraic spaces and generalizations of the motivic Igusazeta function

Jorgo Mandili and Tony Shaska  Computing heights on weighted projective spaces

L. Beshaj and M. Polak  On hyperelliptic curves of genus 3

A. Broughton, T. Shaska and A. Wootton  On automorphisms of algebraic curves

Ismael Cortázar and Antonio F. Costa  On the algebraic classification of subgroups of hyperbolic planar crystallographic groups

Emilio Bujalance, Marston D. E. Conder, Antonio F. Costa and Milagros Izquierdo  On regular dessins d’enfants with 4g automorphisms and a curve of Wiman

Rubén A. Hidalgo  An explicit descent of real algebraic varieties

E. Previato  Curves in isomonodromy and isospectral deformations: Painlevé VI as a case study

Nigel Boston and Jing Hao  Quasiquadratic residue codes and hyperelliptic curves

Gerhard Frey and Tony Shaska  Curves, Jacobians, and cryptography


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This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more.
Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography.
This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.
Graduate students and research mathematicians interested in algebraic geometry, cryptography, and elliptic and hyperelliptic curves.

Articles

Boris M. Bekker and Yuri G. Zarhin  Families of elliptic curves with rational torsion points of even order

Lubjana Beshaj and Scott Guest  The weighted moduli space of binary sextics

Timothy J. Ford  A family of nonnormal double planes associated to hyperelliptic curves

Shuichi Otake and Tony Shaska  On the discriminant of certain quadrinomials

Tim Dokchitser, Vladimir Dokchitser, Céline Maistret and Adam Morgan  Semistable types of hyperelliptic curves

Andrew R. Stout  Formal deformations of algebraic spaces and generalizations of the motivic Igusazeta function

Jorgo Mandili and Tony Shaska  Computing heights on weighted projective spaces

L. Beshaj and M. Polak  On hyperelliptic curves of genus 3

A. Broughton, T. Shaska and A. Wootton  On automorphisms of algebraic curves

Ismael Cortázar and Antonio F. Costa  On the algebraic classification of subgroups of hyperbolic planar crystallographic groups

Emilio Bujalance, Marston D. E. Conder, Antonio F. Costa and Milagros Izquierdo  On regular dessins d’enfants with 4g automorphisms and a curve of Wiman

Rubén A. Hidalgo  An explicit descent of real algebraic varieties

E. Previato  Curves in isomonodromy and isospectral deformations: Painlevé VI as a case study

Nigel Boston and Jing Hao  Quasiquadratic residue codes and hyperelliptic curves

Gerhard Frey and Tony Shaska  Curves, Jacobians, and cryptography