Euler number of the compactified Jacobian and
نویسنده
چکیده
In this paper 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. Introduction Let C be a reduced and irreducible projective curve with singular set Σ ⊂ C and let n : C̃ −→ C be its normalisation. The generalised Jacobian JC of C is an extension of JC̃ by an affine commutative group of dimension δ := dimH0(n∗(OC̃)/OC) = ∑
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