Symplectic $U_7$, $U_8$ and $U_9$ singularities

TL;DR

This paper classifies specific symplectic singularities ($U_7$, $U_8$, $U_9$) using algebraic restrictions and invariants, providing geometric descriptions and distinguishing features.

Contribution

It introduces a classification method for symplectic $U_7$, $U_8$, and $U_9$ singularities based on algebraic restrictions and invariants, with geometric insights.

Findings

Classification of $U_7$, $U_8$, $U_9$ singularities achieved

Discrete invariants effectively distinguish symplectic classes

Geometric descriptions of symplectic classes provided

Abstract

We use the method of algebraic restrictions to classify symplectic $U_7$, $U_8$ and $U_9$ singularities. We use discrete symplectic invariants to distinguish symplectic singularities of the curves. We also give the geometric description of symplectic classes.