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.

arXiv comment32 pages

References in corpus (7)

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• Geometric Manin's Conjecture and rational curves
• Fano varieties in Mori fibre spaces
• Rational curves and instantons on the Fano threefold $Y_5$
• A note on Fano manifolds whose second Chern character is positive
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• Very twisting families of pointed lines on Grassmannians