The spaces of rational curves on del Pezzo threefolds of degree one

TL;DR

This paper proves the irreducibility of moduli spaces of rational curves on general del Pezzo threefolds of degree one, confirming Geometric Manin's conjecture and the enumerativity of specific Gromov-Witten invariants.

Contribution

It establishes the irreducibility of moduli spaces of rational curves on these threefolds, a key step in understanding their geometric properties and enumerative invariants.

Findings

Moduli spaces of rational curves are irreducible on general del Pezzo threefolds of degree one.

Confirmed Geometric Manin's conjecture for these threefolds.

Established enumerativity of certain Gromov-Witten invariants.

Abstract

We prove the irreducibility of moduli spaces of rational curves on a general del Pezzo threefold of Picard rank $1$ and degree $1$. As corollaries, we confirm Geometric Manin's conjecture and enumerativity of certain Gromov-Witten invariants for these threefolds.