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Algebraic Curves and Their Applications
About this Title
Lubjana Beshaj, West Point Military Academy, West Point, NY and Tony Shaska, Oakland University, Rochester, MI, Editors
Publication: Contemporary Mathematics
Publication Year: 2019; Volume 724
ISBNs: 978-1-4704-4247-7 (print); 978-1-4704-5153-0 (online)
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.
Table of Contents
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- 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 Igusa-zeta 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 – Quasi-quadratic residue codes and hyperelliptic curves
- Gerhard Frey and Tony Shaska – Curves, Jacobians, and cryptography