Year: 2026
Type: preprint
Abstract: We study boundary contributions to the holomorphic Lefschetz formula for strict self-maps of compact complex manifolds with a simple normal crossings divisor. At a normally non-resonant boundary fixed point, the local term reduces to the fixed-point problem on the boundary stratum and vanishes in the de Rham specialisation. For resonant points satisfying a normal admissibility condition, finite flat rescaling and relative duality recover the local trace as the coefficient at the excess normal order of a holomorphic family of relative residue traces; in the balanced case, this coefficient is the trace of a class on the special fibre. The numerical coefficient is independent of the admissible presentation. In a coupled family, the de Rham boundary index is the product of the normal contact order and the tangential complete-intersection multiplicity. Boundary contributions to the fixed-point formula for the complement are supported on the resonant fixed points.
Source: arXiv (Cornell University)
Author: Shahsavaripour, Elaheh
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7172020602