【摘要】
The moduli space of complete collineations can be viewed, roughly speaking, as a compactification of the space of linear maps between two fixed vector spaces, whose boundary divisor has simple normal crossings. This space is a spherical wonderful variety. Exploiting its spherical structure, we investigate its birational geometry. In particular, we compute the effective and nef cones, as well as the Mori and moving cones of curves, together with the generators of the Cox ring. Finally, we describe the Mori chamber decomposition of the space of complete collineations of the three-dimensional projective space, recovering as a consequence C. L. Huerta’s description of the Mori chamber decomposition of the space of complete quadric surfaces.
