2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150348We show that the Euler number of the compactified Jacobian of a rational curve $C$ with locally planar singularities is equal to the multiplicity of the $δ$-constant stratum in the base of a semi-universal deformation of $C$. In particular, the multiplicity assigned by Yau, Zaslow and Beauville to a rational curve on a K3 surface $S$ coincides with the multiplicity of the normalisation map in the moduli space of stable maps to $S$.LaTeX, 16 pages with 1 figureAlgebraic Geometrytext