# Discriminantal Arrangement, $3\times3$ Minors of Pl\"ucker Matrix and hypersurfaces in Grassmannian $Gr(3,n)$

## TL;DR

This paper explores the relationship between certain degree 2 hypersurfaces in the Grassmannian $Gr(3,n)$ and generic hyperplane arrangements in $\

## Contribution

It establishes a connection between discriminantal arrangements with triple intersections and specific hypersurfaces in the Grassmannian $Gr(3,n)$.

## Key findings

- Points in these hypersurfaces correspond to hyperplane arrangements with triple intersection multiplicities.
- The work links algebraic geometry of Grassmannians with combinatorial properties of hyperplane arrangements.
- Provides a geometric characterization of arrangements via hypersurfaces in Grassmannian.

## Abstract

We show that points in specific degree 2 hypersurfaces in the Grassmannian $Gr(3, n)$ correspond to generic arrangements of $n$ hyperplanes in $\mathbb{C}^3$ with associated discriminantal arrangement having intersections of multiplicity three in codimension two.