Classification of Local Singularities on Torus Curves of Type (2,5)

TL;DR

This paper provides a topological classification of singularities at the origin for degree 10 torus curves of type (2,5), enhancing understanding of their local geometric structure.

Contribution

It introduces a detailed topological classification of inner singularities on degree 10 torus curves of type (2,5), which was previously unexplored.

Findings

Classification of singularities at the origin for these curves

Identification of different topological types of singularities

Insights into the local structure of torus curves of type (2,5)

Abstract

In this paper, we consider curves of degree 10 of torus type (2,5), C : f_5(x, y)^2 + f_2(x, y)^5 = 0. Assume that f_2(0, 0) = f_5(0, 0) = 0. Then O = (0, 0) is a singular point of C which is called an inner singularity. In this paper, we give a topological classification of singularities of (C,O).