In this paper we show that the Euler number of the compactified Jacobian J̄C 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. The number e(J̄C) is the multiplicity assigned by Beauville to C in his proof of the formula, proposed by Yau and Zaslow, for the number of rational curves on a K3 surface X. We prove that e(J̄C) also coincides with the multiplicity of the normalisation map of C in the moduli space of stable maps to X.

Euler number of the compactified Jacobian and multiplicity of rational curves / Fantechi, Barbara; Goettsche, L.; VAN STRATEN, D.. - In: JOURNAL OF ALGEBRAIC GEOMETRY. - ISSN 1056-3911. - 8:1(1999), pp. 115-133.

Euler number of the compactified Jacobian and multiplicity of rational curves

Fantechi, Barbara;
1999-01-01

Abstract

In this paper we show that the Euler number of the compactified Jacobian J̄C 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. The number e(J̄C) is the multiplicity assigned by Beauville to C in his proof of the formula, proposed by Yau and Zaslow, for the number of rational curves on a K3 surface X. We prove that e(J̄C) also coincides with the multiplicity of the normalisation map of C in the moduli space of stable maps to X.
1999
8
1
115
133
Fantechi, Barbara; Goettsche, L.; VAN STRATEN, D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12994
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