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Transactions of the American Mathematical Society

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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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Additional Information

Bailin Song
Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Email: bailinso@ustc.edu.cn

Received by editor(s): May 3, 2018
Received by editor(s) in revised form: July 1, 2020, and July 9, 2020
Published electronically: February 2, 2021
Additional Notes: The author was supported by National Natrual Science Foundation of China No.11771416
Article copyright: © Copyright 2021 American Mathematical Society