Rational curves on prime Fano threefolds of index 1
arXiv:1808.05590
Abstract
We study the moduli spaces of rational curves on prime Fano threefolds of index 1. For general threefolds of most genera we compute the dimension and the number of irreducible components of these moduli spaces. Our results confirm Geometric Manin's Conjecture in these examples and show the enumerativity of certain Gromov-Witten invariants.
We included the discussion of enumerativity of certain Gromov-Witten invariants. 29 pages. to appear in Journal of Algebraic Geometry