The Laplacian on algebraic threefolds with isolated singularities
Consider a complex projective algebraic threefold \(X\) with isolated singularities. Let \(Y\) the smooth part of \(X\); consider on \(Y\) the induced Fubini-study metric \(g\) and the corresponding Laplacian on \(L^2\)-functions with respect to \(g\). The main result is that on \(Y\) the Laplacian is selfadjoint. The author analyses very carefully the induced Fubini metric in a neighborhood of the singular set using several techniques: resolution of singularities, embedded points, curve blow-ups.
algebraic threefold with isolated singularities
scientific article; zbMATH DE number 695818