Gap sequences of 1-Weierstrass points on non-hyperelliptic curves of genus 10

TL;DR

This paper computes the gap sequences of 1-Weierstrass points on non-hyperelliptic genus 10 curves, classifies their geometric types, and estimates upper bounds for their quantities.

Contribution

It provides the first detailed computation of 1-gap sequences and geometric classification for these specific curves.

Findings

Computed 1-gap sequences for non-hyperelliptic genus 10 curves.

Classified 1-Weierstrass points as flexes, sextactic, and tentactic.

Estimated upper bounds for the number of such points.

Abstract

In this paper, we compute the 1-gap sequences of 1-Weierstrass points on non-hyperelliptic smooth projective curves of genus 10. Furthermore, the geometry of such points is classified as flexes, sextactic and tentactic points. Also, an upper bounds for their numbers are estimated.