Quartic curves in the quintic del Pezzo threefold

Key Points

• The Hilbert scheme of quartic curves on the quintic del Pezzo threefold is smooth and irreducible.
• It is shown that the Hilbert scheme is isomorphic to a Grassmannian bundle over another Hilbert scheme.
• This work builds upon previous studies of rational quartic curves related to the moduli space of stable maps.
• The findings enhance understanding of geometry in the context of rational quartic curves on del Pezzo surfaces.