4.3 – Aut | Walls

A hyperplane $(v{)}^{\perp }$ of ${\mathcal{P}}_S$ such that $$v\in \{x\in S\otimes \mathbb{Q}\mid x\in {\mathcal{R}}_{\mathbb{L}},(x{)}^{\perp }\cap {\mathcal{P}}_S\ne \mathrm{\varnothing }\}$$ is called a wall of a ${\mathcal{P}}_S$-chamber $D$ whenever

$\text{Int}(D)\cap (v{)}^{\perp }=\mathrm{\varnothing }$

and when there exists a non-empty open subset of $(v{)}^{\perp }$
contained in $D\cap (v{)}^{\perp }.$

Walls $(v{)}^{\perp }$ with $⟨v,v{⟩}_S=-2$ are called

$(-2)$-walls.

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