Abstract
The Kodaira Embedding Theorem is extended to Kähler varieties with isolated singularities. UsingL 2 estimates for the bundle-valued\(\bar \partial - operator\), it is shown that a necessary and sufficient condition for a compact normal Kähler variety with isolated singularities to be biholomorphic to a projective-algebraic variety is that the variety admit a holomorphic line bundle that is positive when restricted to the regular part of the variety.
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Vuono, C. The Kodaira Embedding Theorem for Kähler varieties with isolated singularities. J Geom Anal 3, 403–421 (1993). https://doi.org/10.1007/BF02921288
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DOI: https://doi.org/10.1007/BF02921288