Defect of irreducible plane curves with simple singularities
Annales Polonici Mathematici
MSC: Primary 14N25; Secondary 32S25
DOI: 10.4064/ap240405-17-9
Published online: 5 February 2025
Abstract
We focus on the defect of singular plane curves, which was recently introduced by Dimca. Roughly speaking, the defect of a reduced plane curve measures the deviation from being a free curve. We find lower bounds on the defect for certain classes of irreducible plane curves admitting nodes, ordinary cusps and ordinary triple points. The main result states that reduced simply singular plane curves with sufficiently high Arnold exponents are never free.
