Vector bundles induced from jet schemes

Song, Bailin

doi:10.1090/tran/8239

Vector bundles induced from jet schemes
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Trans. Amer. Math. Soc. 374 (2021), 2661-2685 Request permission

Abstract:

A family of holomorphic vector bundles is constructed on a complex manifold $X$. The spaces of the holomorphic sections of these bundles are calculated in certain cases. As an application, if $X$ is an $N$-dimensional compact Kähler 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 $\mathcal N=4$ superconformal vertex algebra with central charge $6$.

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