Rational curves on $V_5$ and rational simple connectedness

Abstract

In this paper the notion of rational simple connectedness for the quintic Fano threefold $V_5\subset {\mathbb{P}}^6$ is studied and unirationality of the moduli spaces ${\overline{M}}_{0,0}^{\text{bir}}(V_5,d)$, with $d\ge 1$, is proved. Many further unirationality results for special moduli spaces of rational curves on quadric hypersurfaces and del Pezzo surfaces are obtained via explicit birational methods.

32 pages

References in corpus (4)

• Rational curves and instantons on the Fano threefold $Y_5$
• A note on Fano manifolds whose second Chern character is positive
• Classification of 2-Fano manifolds with high index
• Very twisting families of pointed lines on Grassmannians