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Euler number of the compactified Jacobian and multiplicity of rational curves

Barbara Fantechi·Lothar Göttsche·Duco van Straten
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Abstract

We 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 $S$.

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Barbara Fantechi, Lothar Göttsche, Duco van Straten. 1997-08-14. Euler number of the compactified Jacobian and multiplicity of rational curves. https://arxiv.org/abs/alg-geom/9708012

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