2022/09/12 by Andrew Burke, Burke, Andrew, Eric Jovinelly +1 · 1 citation
Mathematics · Social Sciences · #14D05 (Secondary) #14H10 #14J45 (Primary) 14J30 #African history and culture studies #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2209.05517
openalex publication_date 2022/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We classify families of free rational curves on all smooth Fano threefolds over the complex numbers. In particular, we prove the family of very free rational curves representing any fixed numerical curve class is either irreducible or empty. This proves Geometric Manin's Conjecture in dimension three. For general Fano threefolds of each deformation type, our results allow us to explicitly count the number of components of the moduli space of irreducible, geometrically rational curves, which may not be free, representing any numerical class.