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

Abstract

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

Keywords

• 1-Weierstrass points
• q-Gap sequence
• Flexes
• Sextactic points
• Tentactic points
• Canonical linear system
• Kuribayashi sextic curve