Geometry of moduli spaces of rational curves in linear sections of Grassmannian $Gr(2,5)$

TL;DR

This paper proves that moduli spaces of low-degree rational curves in linear sections of the Grassmannian Gr(2,5) are rational varieties and explores their compactifications and birational properties.

Contribution

It establishes the rationality of moduli spaces of rational curves of degree up to 3 in linear sections of Gr(2,5), including their compactifications and birational geometry.

Findings

Moduli spaces of degree ≤ 3 rational curves are rational varieties.

Analysis of compactifications of these moduli spaces.

Insights into the birational geometry of the moduli spaces.

Abstract

We prove that the moduli spaces of rational curves of degree at most $3$ in linear sections of the Grassmannian $Gr(2,5)$ are all rational varieties. We also study their compactifications and birational geometry.