2005/01/21 by Donu Arapura, Arapura, Donu · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.math/0501348
openalex publication_date 2005/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given two smooth projective varieties X and Y over a field, we say that X motivates Y if the (suitably defined) motive of Y is contained in the category generated from X by taking sums, summands and products. This notion has appeared implicitly in many places, but it seems useful to make it explicit. Some techniques are given for checking this condition, but in a nutshell it involves building a correspondence which "dominates" Y. Among the more interesting examples dealt with are moduli spaces. We show that in number of cases moduli spaces of sheaves over curves or surfaces are motivated by underly curve or surface. This allows us to check (or recheck) the (generalized) Hodge and Lefschetz standard conjectures for some of these examples. The dominating correspondence in these examples is built from the universal sheaf, and can, in some instances, be realized as a kind of Fourier-Mukai transform.