Description
Book SynopsisThe development of new computational techniques and better computing power has made it possible to attack some classical problems of algebraic geometry. The main goal of this book is to highlight such computational techniques related to algebraic curves. The area of research in algebraic curves is receiving more interest not only from the mathematics community, but also from engineers and computer scientists, because of the importance of algebraic curves in applications including cryptography, coding theory, error-correcting codes, digital imaging, computer vision, and many more.This book covers a wide variety of topics in the area, including elliptic curve cryptography, hyperelliptic curves, representations on some Riemann-Roch spaces of modular curves, computation of Hurwitz spectra, generating systems of finite groups, Galois groups of polynomials, among other topics.
Table of Contents# A New Proof for the Non-Degeneracy of the Frey-Ruck Pairing and a Connection to Isogenies Over the Base Field (E F Schaefer) # Elliptic Curve Torsion Points and Division Polynomials (I A Burhanuddin & M A Huang) # Detecting Complex Multiplication (J D Achter) # Simple Numerical Uniformatization of Elliptic Curves (M Seppala) # On the Moduli Space of Klein Four Covers of the Projective Line (D Glass & R Pries) # Field of Moduli and Field of Definition for Curves of Genus 2 (G Cardona & J Quer) # Explicit Computation of Hurwitz Spectra (R Vogeler) # Non-Normal Bely p-Gonal Surfaces (A Wootton) # Hyperelliptic Curves of Genus 3 with Prescribed Automorphism Group (J Gutierrez et al.) # Curves Over Finite Fields with Many Points: An Introduction (J Voight) # Hyperelliptic Curves of Genus 3 and 4 in Characteristic 2 (Y Demirbas) # Modular Representations on Some Riemann-Roch Spaces of Modular Curves X(N) (D Joyner & A Ksir) # Genus Two Curves Covering Elliptic Curves: A Computational Approach (T Shaska) # A Question About Pic(X) as a G-Module (D Goldstein et al.) # Galois Groups of Prime Degree Polynomials with Nonreal Roots (A Bialostocki & T Shaska) # Counting Generating Systems of a Finite Group from Given Conjugacy Classes (R Staszewski et al.) # Group Action on Genus 3 Curves and Their Weierstrass Points (H Babu & P Venkataraman)
