Moduli spaces of rational curves on Fano threefolds
Roya Beheshti, Brian Lehmann, Eric Riedl, and Sho Tanimoto

TL;DR
This paper classifies components of the moduli space of rational curves on smooth Fano threefolds, confirming a conjecture about their growth and using Geometric Manin's Conjecture to analyze free curves.
Contribution
It proves classification results for moduli space components and confirms Batyrev's conjecture on their growth, advancing understanding of rational curves on Fano threefolds.
Findings
Confirmed Batyrev's conjecture on component growth
Classified moduli space components for rational curves
Applied Geometric Manin's Conjecture to free curves
Abstract
We prove several classification results for the components of the moduli space of rational curves on a smooth Fano threefold. In particular, we prove a conjecture of Batyrev on the growth of the number of components as the degree increases. The key to our approach is Geometric Manin's Conjecture which predicts the number of components parameterizing free curves.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology
