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29 March 2024
 
  » arxiv » math.AG/0003071

 Article overview


A reconstruction of Euler data
Bong H. Lian ; Chien-Hao Liu ; Shing-Tung Yau ;
Date 12 Mar 2000
Subject Algebraic Geometry | math.AG hep-th
AffiliationBrandeis University), Chien-Hao Liu, and Shing-Tung Yau (Harvard University
AbstractWe apply the mirror principle of [L-L-Y] to reconstruct the Euler data $Q={Q_d}_{din{ inyBbb N}cup{0}}$ associated to a vector bundle $V$ on ${smallBbb C}{ m P}^n$ 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 ’{ t 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 $V=T_{ast}{smallBbb C}{ m P}^2$, and $K_d$, $d=1,2,3$, for the bundles ${cal O}_{{ inyBbb C}{ m P}^4}(l)$ with $6le lle 10$ done using the code are also included.
Source arXiv, math.AG/0003071
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