Rational curves on prime Fano threefolds of index 1
Brian Lehmann, Sho Tanimoto
TL;DR
This paper investigates the moduli spaces of rational curves on prime Fano threefolds of index 1, confirming aspects of Geometric Manin's Conjecture and demonstrating the enumerativity of certain Gromov-Witten invariants.
Contribution
It provides explicit computations of the dimension and irreducible components of these moduli spaces for most genera, advancing understanding of rational curves on Fano threefolds.
Findings
Confirmed Geometric Manin's Conjecture for these threefolds
Computed dimensions and components of moduli spaces for general cases
Established enumerativity of specific Gromov-Witten invariants
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology