Moduli spaces of complete collineations are wonderful compactifications of spaces of linear maps of maximal rank between two fixed vector spaces. We investigate the birational geometry of moduli spaces of complete collineations and quadrics from the point of view of Mori theory. We compute their effective, nef and movable cones, the generators of their Cox rings, and their groups of pseudo-automorphisms. Furthermore, we give a complete description of both the Mori chamber and stable base locus decompositions of the effective cone of the space of complete collineations of the 3-dimensional projective space.

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关于完全形式的空间的两边几何：I：归类和二次

完全归类的模空间是两个固定向量空间之间最大秩的线性映射的空间的奇妙压缩。我们从森理论的角度研究完全归一化和二次曲面的模空间的双边几何。我们计算它们的有效锥，可动锥和可动锥，它们的Cox环的生成器以及它们的伪自同构组。此外，我们给出了3维投影空间完全一致空间的有效锥的Mori腔和稳定基轨迹分解的完整描述。