2024/03/12 by Ishan Banerjee, Banerjee, Ishan · 2 citations
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2403.07272
openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove under some simplifying hypotheses questions of Picoco and Levinson-Ullery on Cayley-Bacharach sets. Our results imply that, under suitable hypotheses Cayley-Bacharach sets lie on curves of low degree. We then use these results to estimate error terms to the normalized motive of the space of smooth degree d hypersurfaces in ℙnas d grows to infinity. The error term can be expressed in terms of a certain `sum over points' on plane cubic curves and the associated Hodge structure can be expressed in terms of the cohomology of the moduli space of elliptic curves. We also prove convergence of the motive of degree d hypersurfaces in ℙn as n grows to infinity as well as other results on discriminant complements of high dimensional varieties.