Cohomology of Coherent Sheaves and Series of Supernatural Bundles

TL;DR

This paper demonstrates that the cohomology table of any coherent sheaf on projective space can be expressed as a convergent sum of scaled cohomology tables of supernatural sheaves, revealing a new structural understanding.

Contribution

It introduces the concept of supernatural sheaves and shows their cohomology tables form a basis for decomposing any coherent sheaf's cohomology table.

Findings

Cohomology tables can be decomposed into sums of supernatural sheaves.

The decomposition converges, providing a new analytical tool.

Supernatural sheaves serve as fundamental building blocks for cohomology analysis.

Abstract

We show that the cohomology table of any coherent sheaf on projective space is a convergent--but possibly infinite--sum of positive real multiples of the cohomology tables of what we call supernatural sheaves.