Bulletin of the
Korean Mathematical Society BKMS

Let $Y$ be the quintic del Pezzo $4$-fold defined by the linear section of $\textrm{Gr}(2,5)$ by $\mathbb{P}^7$. In this paper, we describe the locus of double lines in the Hilbert scheme of coincs in $Y$. As a corollary, we obtain the desigularized model of the moduli space of stable maps of degree $2$ in $Y$. We also compute the intersection Poincar\'e polynomial of the stable map space.

Keywords: Rational curves, Fano variety, desingularization, intersection cohomology

MSC numbers: Primary 14E15, 14E08, 14M15, 32S60