Addition via reduction algorithm on trigonal curves

TL;DR

This paper introduces an explicit iterative reduction algorithm for divisor addition on trigonal curves, enabling symbolic computations for curves of various genera, which advances algebraic geometry methods.

Contribution

It presents a new explicit reduction algorithm for divisor addition on trigonal curves, applicable to higher genus cases up to 13 and 14.

Findings

Algorithm successfully performs divisor addition explicitly

Applicable to curves of genus up to 14

Enables symbolic computation in algebraic geometry

Abstract

In this paper we propose a direct and explicit realization of addition of divisors by means of an iterative reduction algorithm. Each iteration of the algorithm is the reduction of a degree $g+1$ divisor to a divisor of degree~$g$. Such an approach allows to carry out all computations explicitly in a symbolic form, which is done for curves $C_{3,4}$, $C_{3,5}$ in this paper, and also for curves of higher genera up to $C_{3,13}$, $C_{3,14}$.