Logarithmic Lefschetz fixed point formulae and resonant boundary indices
arXiv:2607.28288
summary
The paper establishes logarithmic Lefschetz fixed point formulas for strict self‑maps of compact complex manifolds with simple normal‑crossing boundaries, showing how resonant boundary contributions record normal contact and tangential multiplicities.
Abstract
We prove logarithmic Lefschetz fixed point formulae for strict self-maps of compact complex manifolds with simple normal crossings boundary and isolated fixed points. At boundary points, normal rescaling and relative duality give canonical specialisation coefficients for admissible fixed-point ideals. In the de Rham specialisation, non-resonant boundary terms vanish, whereas resonant terms record normal contact and tangential multiplicity.
Topics & keywords
#logarithmic lefschetz formula#compact complex manifolds#simple normal crossings#fixed point theory#resonant boundary termsLefschetz fixed point theoremlogarithmic formsself-mapsde Rham specializationresonancenormal crossing divisor