We complete Mori's program for Kontsevich's moduli space of degree $2$ stable maps to the Grassmannian of lines. We describe all birational models in terms of moduli spaces (of curves and sheaves), incidence varieties, and Kirwan's partial desingularization.
"Mori's Program for the Moduli Space of Conics in Grassmannian." Taiwanese J. Math. 21 (3) 621 - 652, 2017. https://doi.org/10.11650/tjm/7769