Birational geometry of the moduli space of rank 2 parabolic vector bundles on a rational curve

TL;DR

This paper explores the birational geometry of the moduli space of rank 2 semistable parabolic vector bundles on a rational curve, computing the effective cone and describing all Mori's program models as related moduli spaces.

Contribution

It provides a detailed analysis of the birational structure and effective cone of these moduli spaces, linking Mori's models to moduli spaces with specific parabolic weights.

Findings

Computed the effective cone of the moduli space

Identified all Mori's program models as moduli spaces with particular weights

Established the birational relationships among these moduli spaces

Abstract

We investigate the birational geometry (in the sense of Mori's program) of the moduli space of rank 2 semistable parabolic vector bundles on a rational curve. We compute the effective cone of the moduli space and show that all birational models obtained by Mori's program are also moduli spaces of parabolic vector bundles with certain parabolic weights.