A family of holomorphic vector bundles is constructed on a complex manifold $X$. The space of the holomorphic sections of these bundles are calculated in certain cases. As an application, if $X$ is an $N$-dimensional compact K\"ahler manifold with holonomy group $SU(N)$, the space of holomorphic vector fields on its jet scheme $J_m(X)$ is calculated. We also prove that the space of the global sections of the chiral de Rham complex of a K3 surface is the simple $N=4$ superconformal vertex algebra with central charge $6$.

中文翻译：

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由喷射方案引起的矢量丛

在复流形 $X$ 上构造了一个全纯向量丛族。在某些情况下计算这些束的全纯截面的空间。作为一个应用，如果$X$是一个$N$维紧致K\"ahler流形，具有完整群$SU(N)$，则计算其喷射方案$J_m(X)$上的全纯向量场空间。我们还证明了 K3 表面的手性 de Rham 复合体的全局部分的空间是简单的 $N=4$ 超共形顶点代数，中心电荷 $6$。