Iitaka fibrations and integral points: a family of arbitrarily polarized spherical threefolds

2025/05/15 by Ulrich Derenthal, Florian Wilsch, Derenthal, Ulrich +1
Mathematics · Physics and Astronomy · #11D45 (14G05 #11G35) #14M27 #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2505.10245

openalex publication_date 2025/05/15 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

Studying Manin's program for a family of spherical log Fano threefolds, we determine the asymptotic number of integral points whose height associated with an arbitrary ample line bundle is bounded. This confirms a recent conjecture by Santens and sheds new light on the logarithmic analogue of Iitaka fibrations, which have not yet been adequately formulated.

Citations

• Manin's conjecture for integral points on toric varieties
• Integral Points on a del Pezzo Surface over Imaginary Quadratic Fields
• The Distribution of Integral Points on the Wonderful Compactification by Height
• Integral points of bounded height on a log Fano threefold
• Counting imaginary quadratic points via universal torsors
• Igusa integrals and volume asymptotics in analytic and adelic geometry
• Counting integral points on universal torsors
• The total coordinate ring of a wonderful variety
• Tamagawa numbers of polarized algebraic varieties
• Hauteurs et mesures de Tamagawa sur les variétés de Fano
• Rational points of bounded height on Fano varieties

Related

• Integral points of bounded height on a log Fano threefold
• Manin's conjecture for integral points on toric varieties
• The Manin-Peyre conjecture for smooth spherical Fano threefolds
• The Manin–Peyre conjecture for smooth spherical Fano threefolds
• Effective log Iitaka fibrations for surfaces and threefolds