November 9, 2025Open Access

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.

Abstract

We investigate the Hilbert scheme of points on curves with n-fold singularities, that is curves that look locally around their singular points as the axis in an affine space. We describe the structure and number of its irreducible components, and provide a detailed analysis of their singularities, revealing rich combinatorial patterns governing its geometry.

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

Key Points

Abstract

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