Reduction of superelliptic Riemann surfaces

Author:

Shaska Tanush

Abstract

For a superelliptic curve X \mathcal {X} , defined over Q \mathbb {Q} , let p \mathfrak {p} denote the corresponding moduli point in the weighted moduli space. We describe a method how to determine a minimal integral model of X \mathcal {X} such that: i) the corresponding moduli point p \mathfrak {p} has minimal weighted height, ii) the equation of the curve has minimal coefficients. Part i) is accomplished by reduction of the moduli point which is equivalent with obtaining a representation of the moduli point p \mathfrak {p} with minimal weighted height, as defined in \cite{b-g-sh}, and part ii) by the classical reduction of the binary forms.

Publisher

American Mathematical Society

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1. EMMA PREVIATO AND HER MATHEMATICAL LIFE (1952-2022);Albanian Journal of Mathematics;2023-06-15

2. ON THE STABILITY OF BINARY FORMS AND THEIR WEIGHTED HEIGHTS;Albanian Journal of Mathematics;2022-06-15

3. The engaging symmetry of Riemann surfaces: A historical perspective;Contemporary Mathematics;2022

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