The perverse filtration and the Lefschetz hyperplane theorem, II

TL;DR

This paper explores the perverse filtration in cohomology, linking it to restriction kernels via the Lefschetz hyperplane theorem, and discusses implications for mixed Hodge theory and intersection cohomology.

Contribution

It provides a new interpretation of the perverse filtration using restriction kernels and derives mixed-Hodge-theoretic consequences for intersection cohomology.

Findings

Perverse filtration characterized via kernels of restriction maps

Derived consequences for mixed Hodge structures in intersection cohomology

Enhanced understanding of the decomposition theorem

Abstract

The perverse filtration in cohomology and in cohomology with compact supports is interpreted in terms of kernels of restrictions maps to suitable subvarieties by using the Lefschetz hyperplane theorem and spectral objects. Various mixed-Hodge-theoretic consequences for intersection cohomology and for the decomposition theorem are derived.