LOG BAUM–BOTT RESIDUES FOR FOLIATIONS BY CURVES

The paper’s Theorem 1.2 states exactly the three claims the candidate addresses: (i) existence of local logarithmic Baum–Bott residues along each connected component S_λ ⊂ Sing(F) ∩ D; (ii) a global localization formula on compact X equating ∫_X φ(TX(−log D) − TF) to the sum of Baum–Bott residues off D plus the new log-residues along D; and (iii) an explicit isolated-point Grothendieck residue formula using the matrix Mlog(ϑ) built from a Saito frame and the bracket structure constants. These appear verbatim in the statement and development of Theorem 1.2 and its proof, including the definition of Mlog(ϑ) and the global decomposition via Alexander duality and Bott vanishing . The candidate’s proof uses a classical Chern–Weil/Chern–Simons transgression plus Bott-partial-connection argument to make the top-degree form exact on X\Sing(F), then applies Stokes to localize to boundary integrals, and finally identifies these with Grothendieck residues in a Saito frame—precisely mirroring the paper’s outcome (the paper formalizes this via a relative Čech–de Rham cocycle, Bott vanishing, and the Alexander isomorphism; the local residue is computed using the matrix Mlog(ϑ)) . The methods differ in presentation (Chern–Simons/Stokes vs. relative Čech–de Rham/Alexander), but the logical content and formulas match, including the simplification to Jlogϑ in the normal crossings case . Thus, both are correct; they are essentially equivalent derivations framed through different standard formalisms.