# A blowup algebra of hyperplane arrangements

## TL;DR

This paper establishes a deep algebraic connection between the Orlik-Terao algebra and the blowup algebra of certain ideals associated with hyperplane arrangements, proving Cohen-Macaulay properties and fiber-type structure.

## Contribution

It demonstrates that the Rees algebra of the ideal generated by hyperplane arrangement products is of fiber-type and Cohen-Macaulay, linking it to the Orlik-Terao algebra.

## Key findings

- Orlik-Terao algebra is isomorphic to the special fiber of the ideal
- Rees algebra of the ideal is Cohen-Macaulay and of fiber-type
- Provides an alternative proof of Cohen-Macaulayness of the Orlik-Terao algebra

## Abstract

It is shown that the Orlik-Terao algebra is graded isomorphic to the special fiber of the ideal $I$ generated by the $(n-1)$-fold products of the members of a central arrangement of size $n$. This momentum is carried over to the Rees algebra (blowup) of $I$ and it is shown that this algebra is of fiber-type and Cohen-Macaulay. It follows by a result of Simis-Vasconcelos that the special fiber of $I$ is Cohen-Macaulay, thus giving another proof of a result of Proudfoot-Speyer about the Cohen-Macauleyness of the Orlik-Terao algebra.