Jumping numbers of a unibranch curve on a smooth surface
Daniel Naie
TL;DR
This paper presents a formula for calculating the jumping numbers of a unibranch curve on a smooth surface, linking them to the Enriques diagram or semigroup generators of the singularity.
Contribution
It introduces a new formula that relates jumping numbers to the Enriques diagram and semigroup generators for unibranch curve singularities.
Findings
Formula for jumping numbers expressed via Enriques diagram
Connection between jumping numbers and semigroup generators
Provides a method to compute jumping numbers explicitly
Abstract
A formula for the jumping numbers of a curve unibranch at a singular point is established. The jumping numbers are expressed in terms of the Enriques diagram of the log resolution of the singularity, or equivalently in terms of the canonical set of generators of the semigroup of the curve at the singular point.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory