Moduli spaces of rational curves on Fano threefolds

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.

arXiv commentNo change from the previous version, 51 pages, to appear in Advances in Mathematics