Canonical cohomology as an exterior module

TL;DR

This paper demonstrates that the total cohomology of the canonical bundle of a smooth projective variety, viewed as an exterior algebra module, decomposes into a direct sum of simpler, well-structured submodules, enhancing earlier results.

Contribution

It introduces a new decomposition of the canonical cohomology as an exterior module, providing a clearer structural understanding and improving previous theorems.

Findings

Cohomology splits into direct sum of submodules

Submodules are generated in degree zero

Submodules have linear free resolutions

Abstract

We show that the total cohomology of the canonical bundle of a smooth projective variety, seen as a module over an exterior algebra, splits into a natural direct sum of submodules which are generated in degree zero and have a linear free resolution. This improves a previous result of the first two authors.