  Let $Y$ be the del Pezzo $4$-fold defined by the linear section
$\textrm{Gr}(2,5)$ by $\mathbb{P}^7$. In this paper, we classify the type of
normal bundles of lines in $Y$ and describe its parameter space. As a
corollary, we obtain the desigularized model of the moduli space of stable maps
in $Y$. Also we compute the intersection Poincar\'e polynomial of the stable
maps space.

Algebraic Geometry