Let X be a projective scheme over a field k , and
$0\rightarrow F'\rightarrow F \rightarrow F''\rightarrow 0$ be a short exact sequence of semi-stable sheaves with same reduced Hilbert polynomial.
I want to find a flat family $E$ of semi stable sheaves parametrized by affine line $A^1$ such that
$E_0 \simeq F'\bigoplus F''$
$E_t\simeq F $ for all $t\in A^1\setminus \lbrace 0\rbrace$
and this problem is in Lemma 8.3.4 in this PDF
In this PDF,what is
"the coherent sheaf over X × $A^1$ given by this extension class."?