Euler number of the compactified Jacobian and multiplicity of rational curves
Euler number of the compactified Jacobian and multiplicity of rational curves
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紧致雅可比行列式的欧拉数和有理曲线的重数
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
D. Straten
中科院分区：
文献类型：
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作者：
B. Fantechi;L. Gottsche;D. Straten
证明了具有局部平面奇点的有理曲线$C$的紧化雅可比矩阵的欧拉数等于$C$的半泛变形基上的$-不变层的重数.特别地，Yau，Zaslow和Beauville赋予K3曲面上有理曲线$S$的重数与稳定映射的模空间中的正规化映射到$S$的重数重合。
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 $\delta$-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 $S$.