Split extension as a degeneration
= Split extension as a degeneration
= Splitting an extension gives a module degeneration
{synonym}
An extension's vertexwise split arrow matrices are $\left(\begin{smallmatrix}f_X&\xi\\0&f_Z\end{smallmatrix}\right)$. Scaling the subobject by $t$ multiplies $\xi$ by $t$. Nonzero $t$ preserves the middle isomorphism class; $t=0$ gives $X\oplus Z$. For a nonsplit extension, the split orbit is distinct and lies in the smaller-dimensional boundary of the middle orbit closure.