A reconstruction of Euler data

Bong H. Lian Brandeis University Chien-Hao Liu Harvard University Shing-Tung Yau Harvard University

mathscidoc:1608.01032

2000
We apply the mirror principle of [L-L-Y] to reconstruct the Euler data $Q=\{Q_d\}_{d \in{\tinyBbb N}\cup\{0\}}$ associated to a vector bundle V on ${\smallBbb C}{\rm P}^n$ and a multiplicative class b . This gives a direct way to compute the intersection number $K_d$ without referring to any other Euler data linked to $Q$ . Here $K_d$ is the integral of the cohomology class $b(V_d )$ of the induced bundle $V_d$ on a stable map moduli space. A package '{\tt \verb+EulerData_MP.m+}' in Maple V that carries out the actual computation is provided. For b the Chern polynomial, the computation of $K_1$ for the bundle $V=T_{\ast}{\smallBbb C}{\rm P}^2$, and $K_d, d=1,2,3$, for the bundles ${\cal O}_{{\tinyBbb C}{\rm P}^4}(l)$ with 6≤l≤10 done using the code are also included.
Euler data, Chern polynomial, bundles
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@inproceedings{bong2000a,
  title={A reconstruction of Euler data},
  author={Bong H. Lian, Chien-Hao Liu, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160828172615506822497},
  year={2000},
}
Bong H. Lian, Chien-Hao Liu, and Shing-Tung Yau. A reconstruction of Euler data. 2000. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160828172615506822497.
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