On the Zariski invariant of plane branches
                    
                    
                        Annales Polonici Mathematici                     
                                        
                        MSC: Primary 14H20; Secondary 14H50, 14B05                    
                                        
                        DOI: 10.4064/ap240627-22-1                    
                                            
                            Published online: 4 April 2025                        
                                    
                                                Abstract
We show how to obtain the Zariski invariant of a plane branch employing the contact order or the intersection multiplicity with elements in a particular family of curves, and we present some consequences of this result.
 
             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                         
                                                            