Canonical and Hodge-polarized Mezzoperversities for Fubini-study Iterated Wedge Metrics on Complex Projective Varieties
Year: 2026
Type: preprint
Abstract: Let X ⊂ CP N be a complex projective variety equipped with a fixed Thom-Mather stratification, and let gFS be the induced Fubini-Study iterated wedge metric on X reg . In [Luo26b, Luo26a] we construct, via iterated Calderón constructions, a canonical mezzoperversity Wcan and identify the L 2 de Rham cohomology of the corresponding canonical closed extension with IH • Wcan (X). In [Luo26c] we construct a polarized Hodge mezzoperversity W polHdg and prove ICW polHdg ∼ = IC m. In this paper we prove the analytic comparison Wcan = W polHdg without additional hypotheses. Consequently, for arbitrary stratification depth, the canonical L 2 de Rham cohomology of (X reg , gFS) identifies with the middle intersection cohomology IH • m(X ), thereby verifying the Cheeger-Goresky-MacPherson conjecture in this setting.
Source: HAL
Author: Luo, Jiaming
Institution: Kashi University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7135157680