Hilbert schemes of points on fold-like curves and their combinatorics

Key Points

• The findings reveal intricate relationships among singularities and geometry, highlighting combinatorial systematics.
• Analysis identifies the number and structure of irreducible components in the Hilbert scheme of points.
• The study employs theoretical methods to explore curves with n-fold singularities and their geometric implications.
• These insights suggest potential avenues for further research into singularity behavior and its combinatorial geometry.