Perturbations of intersection multiplicity

Key Points

• The central aim is to introduce a new computable invariant for plane curve singularities and assess its role in stability.
• Introduced a new invariant λ(f, g) for any pair of plane curve singularities.
• Mathematically analyzed how intersection multiplicity behaves under perturbations of these curves.
• Established conditions under which intersection multiplicity remains stable, specifically for perturbations of degree at least λ(f, g).
• Proved that the intersection multiplicity of the curves f and g is stable under certain perturbations.
• Demonstrated that stability holds true for perturbations of degree equal to or greater than the invariant λ(f, g).