Rational curves on V₅ and rational simple connectedness

2019/01/21 by Andrea Fanelli, Fanelli, Andrea, Laurent Gruson +3 · 2 citations
Mathematics · #14E05 #14H10 #14J45 #14M20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions #math.AG #msc:14E05 #msc:14H10 #msc:14J45 #msc:14M20

paper · pdf · doi:10.48550/arxiv.1901.06930

32 pages

arxiv created 2019/01/21 · openalex publication_date 2019/01/21 · arxiv updated 2019/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper the notion of rational simple connectedness for the quintic Fano threefold V₅⊂ ℙ⁶ is studied and unirationality of the moduli spaces M_0,0^bir(V₅,d), with d ≥ 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.

Cited by

• The spaces of rational curves on del Pezzo surfaces via conic bundles
• Quartic curves in the quintic del Pezzo threefold

Related

• Moduli spaces of rational curves on Fano threefolds
• Balanced rational curves and minimal rational connectedness of Fano hypersurfaces
• Linear growth and moduli spaces of rational curves
• Rational curves on prime Fano threefolds of index 1
• Fano varieties and linear sections of hypersurfaces