Tschirnhaus-Weierstrass curves
Josef Schicho, David Sevilla
TL;DR
The paper introduces Tschirnhaus-Weierstrass curves, a unique form for pointed curves that simplifies the computation of isomorphisms between algebraic curves.
Contribution
It defines the Tschirnhaus-Weierstrass form for pointed curves and proves its uniqueness up to scaling, aiding in isomorphism computations.
Findings
Every pointed curve has a Tschirnhaus-Weierstrass form.
The form is unique up to a scaling of variables.
This representation facilitates isomorphism calculations.
Abstract
We define the concept of Tschirnhaus-Weierstrass curve, named after the Weierstrass form of an elliptic curve and Tschirnhaus transformations. Every pointed curve has a Tschirnhaus-Weierstrass form, and this representation is unique up to a scaling of variables. This is useful for computing isomorphisms between curves.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Advanced Numerical Analysis Techniques