Nef Cones of Hilbert Schemes of Orthogonal Grassmannians

We show the number of connected components of the Hilbert scheme of orthogonal Grassmannians under certain condition, and use this result to describe the geometry of the Hilbert scheme. Subsequently, we determine the Nef cone of the Hilbert scheme by identifying curves dual to the generators of its Neron-Severi group. Our results generalize those of ordinary Grassmannians by Seong, and our approach adapts his proof technique alongside relevant Schubert calculus.