Variation of the Green function on Riemann surfaces and Whitney's holomorphic stratification conjecture (Q1812699)

Let \(M\) be a Riemann surface. In this work, the authors study how the Green function on \(M\) varies when the conformal structure changes. Making use of this, the authors deal with the Whitney's conjecture for complex projective algebraic varieties making use of an interpolation formula of H. Whitney and proving that: Any complex algebraic subvariety of \(\mathbb{C}\mathbb{P}^ n\) admits a finite partition (stratification) \({\mathcal S}\) into holomorphic submanifolds such that, for each \(S\) in \({\mathcal S}\), every point of \(S\) has a neighborhood in \(\mathbb{C}\mathbb{P}^ n\) that may be foliated by \((\dim S)\)-dimensional holomorphic leaves that respect the strata.