I just downloaded "Degeneration in discriminantal arrangements", by Saito, Takuya from the journal "Advances in applied mathematics" dated November 2025 and fed it to Claude.
It not only explained the math but created a react app to demonstrate it. I'm not that can be explained by regurgitating part of it with noise.
I encourage you to try it with something of your own.
Abstract:
Discriminantal arrangements are hyperplane arrangements
that are generalization of braid arrangements. They are con-
structed from given hyperplane arrangements, but their com-
binatorics are not invariant under combinatorial equivalence.
However, it is known that the combinatorics of the discrimi-
nantal arrangements are constant on a Zariski open set of the
space of hyperplane arrangements. In the present paper, we
introduce (T, r)-singularity varieties in the space of hyper-
plane arrangements to classify discriminantal arrangements
and show that the Zariski open set is the complement of
(T, r)-singularity varieties. We study their basic properties
and operations and provide examples, including infinite fami-
lies of (T, r)-singularity varieties. In particular, the operation
that we call degeneration is a powerful tool for constructing
(T, r)-singularity varieties. As an application, we provide a
list of (T, r)-singularity varieties for spaces of small line ar-
rangements.
* https://doi.org/10.1016/j.aam.2025.103001
* https://imgur.com/jjfFNMI.png