2025/02/17 by Loïs Faisant, Faisant, Loïs
Computer Science · Engineering · Mathematics · #11G50 #14E18 #14G40 #14H10 #14J45 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2502.11704
openalex publication_date 2025/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the formalism of Cox rings and universal torsors, we prove a decomposition of the Grothendieck motive of the moduli space of morphisms from an arbitrary smooth projective curve to a Mori Dream Space (MDS). For the simplest cases of MDS, that of toric varieties, we use this decomposition to prove an instance of the motivic Batyrev--Manin--Peyre principle for curves satisfying tangency conditions with respect to the boundary divisors, often called Campana curves.