Kontsevich spaces of rational curves on Fano hypersurfaces

2014/09/12 by Eric Riedl, David Yang, Riedl, Eric +1 · 4 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1409.3802

openalex publication_date 2014/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the spaces of rational curves on a general hypersurface. In particular, we show that for a general degree d hypersurface in ℙⁿ with n ≥ d+2, the space M_0,0(X,e) of degree e Kontsevich stable maps from a rational curve to X is an irreducible local complete intersection stack of dimension e(n-d+1)+n-4.

Citations

• Fano varieties and linear sections of hypersurfaces

Cited by

• Homological stability and weak approximation
• Rational surfaces on low degree hypersurfaces
• Dimension of the space of conics on Fano hypersurfaces
• A short way of counting maps to hypersurfaces in Grassmannians

Related

• Rational curves on hypersurfaces of low degree
• A note on rational curves on general Fano hypersurfaces
• The Kodaira dimension of spaces of rational curves on low degree hypersurfaces
• Interpolation of curves on Fano hypersurfaces
• Geometry of Rational Curves on Low degree Complete Intersections