Polydiagonal compactification of configuration spaces
Polydiagonal compactification of configuration spaces
复制标题
配置空间的多对角压缩
DOI：
10.1090/s1056-3911-01-00293-4
复制
发表时间：
1999
影响因子：
1.8
通讯作者：
A. Ulyanov
中科院分区：
文献类型：
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作者：
A. Ulyanov
光滑代数簇X中n个不同标记点的位形空间的光滑紧化X <n>是由一个自然的爆破序列构造的，在每个阶段都表现出置换群Sn的完全对称性。用水平树标记了无穷远处正规交叉因子的层次，并研究了层次的结构。这是De Concini-Procesi意义下的极大奇妙紧化，并且它在Fulton-MacPherson紧化上有一个层相容的满射。在紧化中加入的简并构型用类似于富尔顿和麦克弗森的多屏几何描述。在特征为0时，Sn作用于X的各向同性子群是阿贝尔群，因此X可能是朝向对称乘积X/Sn的奇点的显式分解的一步。
A smooth compactification X〈n〉 of the configuration space of n distinct labeled points in a smooth algebraic variety X is constructed by a natural sequence of blowups, with the full symmetry of the permutation group Sn manifest at each stage. The strata of the normal crossing divisor at infinity are labeled by leveled trees and their structure is studied. This is the maximal wonderful compactification in the sense of De Concini–Procesi, and it has a strata-compatible surjection onto the Fulton–MacPherson compactification. The degenerate configurations added in the compactification are geometrically described by polyscreens similar to the screens of Fulton and MacPherson. In characteristic 0, isotropy subgroups of the action of Sn on X〈n〉 are abelian, thus X〈n〉 may be a step toward an explicit resolution of singularities of the symmetric products X/Sn.