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. In this talk, we introduce wall-crossings of the moduli space, sl2-conformal blocks and double sequences that are central techniques for the computation of the effective cone. This is a joint work with Dr. Han-Bom Moon.
