The Laplacian on algebraic threefolds with isolated singularities
We give a complete description of the induced Fubini-Study metric (up to quasi-isometry) in a neighbourhood of an isolated complex projective threefold singularity, by using a sufficiently high resolution of singularities. This is then used to prove the self-adjointness of the corresponding Laplacian acting on square integrable functions, on the non-compact smooth locus of complex projective threefolds with isolated singularities.
Volume 130, 2020
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