Residues and currents from singular forms on complex manifolds
Review article, 2026
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.
currents
Residues
divergent integrals
Author
Mattias Lennartsson
Chalmers, Mathematical Sciences, Algebra and geometry
University of Gothenburg
Complex Variables and Elliptic Equations
1747-6933 (ISSN) 1747-6941 (eISSN)
Vol. 71 9 1747-1770Subject Categories (SSIF 2025)
Mathematical Analysis
DOI
10.1080/17476933.2025.2553112