POLARIZED HODGE MEZZOPERVERSITIES AND THE MIDDLE INTERSECTION COMPLEX FOR FUBINI-STUDY WEDGE METRICS ON STRATIFIED PROJECTIVE VARIETIES

Let X ⊂ CP N be a Thom-Mather stratified projective variety, and endow X reg with the induced Fubini-Study iterated wedge metric. Closed extensions of the L 2 de Rham operator are encoded by mezzoperversities (ideal boundary conditions) along the singular strata. Building on the canonical analytic mezzoperversity Wcan defined via iterated Calderón projectors, we supply the Hodge-theoretic input for the middle criterion. For each stratum with nontrivial trace bundle we construct an incidence-compatible polarized Hodge structure on the trace bundle; its Weil involution singles out a Lagrangian subbundle W mid ⊂ H. These data assemble into a canonical self-dual mezzoperversity W mid with associated Deligne sheaf canonically isomorphic to the middle intersection complex IC m. The analytic identification Wcan = W mid is treated in a companion paper.