A transcendental approach to injectivity theorem for log canonical pairs

TL;DR

This paper develops an analytic approach using harmonic integrals and L2 methods to prove an injectivity theorem for log canonical pairs, extending classical results to complex analytic contexts.

Contribution

It introduces a transcendental, analytic proof of the injectivity theorem for log canonical pairs, broadening its applicability beyond algebraic geometry.

Findings

Established an analytic proof of the injectivity theorem for purely log terminal pairs.

Generalized the injectivity theorem to the complex analytic setting.

Utilized harmonic integrals and L2 methods for the dbar-equation in the proof.

Abstract

In this paper, we study transcendental aspects of the cohomology groups of adjoint bundles of log canonical pairs, aiming to establish an analytic theory for log canonical singularities. As a result, in the case of purely log terminal pairs, we give an analytic proof of the injectivity theorem originally proved by the Hodge theory. Our method is based on the theory of harmonic integrals and the L2-method for the dbar-equation, and it enables us to generalize the injectivity theorem to the complex analytic setting.