Vector bundles induced from jet schemes
Copyright policy )Vector bundles induced from jet schemes
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 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 $N=4$ superconformal vertex algebra with central charge $6$.
25 pages
- University of Science and Technology of China China (People's Republic of)
Mathematics - Differential Geometry, holomorphic vector bundles, Compact Kähler manifolds: generalizations, classification, holomorphic sections, 53C07, Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions, Differential Geometry (math.DG), Holomorphic bundles and generalizations, Sheaves and cohomology of sections of holomorphic vector bundles, general results, holomorphic vector fields, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Representation Theory
Mathematics - Differential Geometry, holomorphic vector bundles, Compact Kähler manifolds: generalizations, classification, holomorphic sections, 53C07, Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions, Differential Geometry (math.DG), Holomorphic bundles and generalizations, Sheaves and cohomology of sections of holomorphic vector bundles, general results, holomorphic vector fields, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Representation Theory
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