A note on free determinantal hypersurface arrangements in $\mathbb{P}^{14}_{\mathbb{C}}$

TL;DR

This paper investigates specific determinantal hypersurface arrangements in complex projective 14-space, demonstrating their freeness through the analysis of arrangements derived from 3-minors of a generic matrix.

Contribution

It introduces and proves the freeness of particular determinantal arrangements in high-dimensional projective space, expanding understanding of free hypersurface arrangements.

Findings

Certain determinantal arrangements are free hypersurfaces.

The arrangements are constructed from 3-minors of a generic 3x5 matrix.

The study provides new examples of free arrangements in complex projective space.

Abstract

In the present note we study determinantal arrangements constructed with use of the $3$-minors of a $3 \times 5$ generic matrix of indeterminates. In particular, we show that certain naturally constructed hypersurface arrangements in $\mathbb{P}^{14}_{\mathbb{C}}$ are free.