Moduli spaces of rational curves on Artin-Mumford double solids

TL;DR

This paper characterizes the structure of moduli spaces of rational curves on Artin-Mumford double solids, providing the first example of Fano varieties with multiple Manin components per degree, advancing understanding of rational curves on complex varieties.

Contribution

It describes the irreducible components of these moduli spaces, offering the first example of Fano varieties satisfying Geometric Manin's Conjecture with multiple components.

Findings

Identification of irreducible components of moduli spaces

First example of Fano varieties with multiple Manin components

Supports Geometric Manin's Conjecture in new context

Abstract

We describe the irreducible components of the moduli spaces of rational curves on Artin-Mumford double solids. This provides the first example of Fano varieties that satisfy Geometric Manin's Conjecture with multiple Manin components in moduli space of rational curves for each degree.