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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 ofnormal bundles of lines in $Y$ and describe its parameter space. As acorollary, we obtain the desigularized model of the moduli space of stable mapsin $Y$. Also we compute the intersection Poincar\'e polynomial of the stablemaps space.

Double lines in the quintic del Pezzo fourfold