Free divisors and rational cuspidal plane curves
Alexandru Dimca, Gabriel Sticlaru
TL;DR
This paper characterizes free divisors in plane curves using the Hilbert function of the Milnor algebra and presents new examples of rational cuspidal curves that are free, proposing related conjectures.
Contribution
It provides a new characterization of freeness for plane curves and introduces numerous new free rational cuspidal curves, along with conjectures on their properties.
Findings
Characterization of freeness via Hilbert function
New examples of free rational cuspidal curves
Proposed conjectures on stronger properties
Abstract
A characterization of freeness for plane curves in terms of the Hilbert function of the associated Milnor algebra is given as well as many new examples of rational cuspidal curves which are free. Some stronger properties are stated as conjectures.
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