Residues and currents from singular forms on complex manifolds

Review article, 2025

Using methods from the theory of residue currents we provide asymptotic expansions of certain divergent integrals on complex manifolds. We express the coefficients in these expansions with the conjugate Dolbeault residue, introduced by Felder and Kazhdan [Divergent integrals, residues of Dolbeault forms and asymptotic riemann mappings. Int Math Res Not. (8), 2016], and define a new residue which we call the Aeppli residue.