A corollary to Kodaira-Spencer’s theorem on continuity of eigenvalues
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We give an elementary proof of continuity of the determinant in the parameter for a smooth family of laplacians (of the same nullity) on a smooth family of holomorphic vector bundles over a compact complex manifold. Families of unitary flat bundles over a compact Riemann surface are discussed, as an example.
KeywordsVector Bundle Zeta Function Complex Manifold Compact Riemann Surface Holomorphic Vector Bundle
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