The irreducibility of the spaces of rational curves on del Pezzo manifolds

TL;DR

This paper proves the irreducibility of rational curve spaces on certain del Pezzo manifolds and confirms Geometric Manin's Conjecture for these cases, advancing understanding in algebraic geometry.

Contribution

It establishes the irreducibility of rational curves on del Pezzo manifolds of Picard rank 1 and dimension ≥4, and verifies Geometric Manin's Conjecture in these contexts.

Findings

Spaces of rational curves are irreducible on specified del Pezzo manifolds.

Confirmed Geometric Manin's Conjecture for these manifolds.

Analyzed fibers of evaluation maps to achieve results.

Abstract

We prove the irreducibility of the spaces of rational curves on del Pezzo manifolds of Picard rank 1 and dimension at least 4 by analyzing the fibers of evaluation maps. As a corollary, we prove Geometric Manin's Conjecture in these cases.