Vector bundles induced from jet schemes

Song, Bailin

doi:10.1090/tran/8239

Vector bundles induced from jet schemes

Author: Bailin Song
Journal: Trans. Amer. Math. Soc. 374 (2021), 2661-2685
MSC (2020): Primary 17B69, 53C07, 32L10
DOI: https://doi.org/10.1090/tran/8239
Published electronically: February 2, 2021
MathSciNet review: 4223029
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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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