Rational surfaces on low degree hypersurfaces

2025/08/26 by Browning, Tim, Yamagishi, Shuntaro
#14G05 #14H10 (11P55 #14J26 #14J70) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.18938

Abstract

We use function field analytic number theory to establish the irreducibility and dimension of the moduli space that parameterises morphisms of fixed degree from ℙ² to an arbitrary smooth hypersurface of sufficiently small degree.

Citations

• Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method
• Rational curves on complete intersections and the circle method
• A higher genus circle method and an application to geometric Manin's conjecture
• A motivic circle method
• A geometric version of the circle method
• Kontsevich spaces of rational curves on Fano hypersurfaces
• Bihomogeneous forms in many variables
• The connectedness of the moduli space of maps to homogeneous spaces

Related

• Associated form morphism
• Rational curves on hypersurfaces of low degree, II
• A higher genus circle method and an application to geometric Manin's conjecture
• Low degree subvarieties of universal hypersurfaces
• The Moduli Space of Totally Marked Degree Two Rational Maps