Making conical compactifications wonderful
Making conical compactifications wonderful
复制标题
使圆锥形压实变得美妙
DOI：
10.1007/s000290050027
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
C. Procesi
中科院分区：
文献类型：
--
作者：
R. Macpherson;C. Procesi
设M是复流形。假设我们给定M的一个“锥”紧化X（见下面的定义1），这大致意味着X上的每一点都有一个邻域，其中X-M具有锥的结构。本文构造了M的一个“极小奇妙”紧化X。紧化X是奇妙的（[D-P2]），因为X-M是一个在X中具有正规交叉的因子。此外，X是由X通过沿着层爆破得到的奇紧化中的极小的，文献中的几个有趣的紧化都是本文构造的极小奇紧化X的例子.其中包括[D-P2]，[D-P3]的对称簇的紧化，[FM]的构形空间的紧化，[D-P1]的线性子空间的补的排列的紧化。有关这些示例，请参阅§ 4。
Let M be a complex manifold. Suppose we are given a compactification X of M that is “conical”(Def. 1 below), which means roughly that every point on X has a neighborhood in which X− M has the structure of a cone. In this paper we construct a “minimal wonderful” compactification X of M. The compactification X is wonderful ([D-P2]) in the sense that X− M is a divisor with normal crossings in X. Furthermore, X is minimal among the wonderful compactifications obtained from X by blowing up along strata.Several interesting compactifications in the literature turn out to be examples of the minimal wonderful compactification X constructed in this paper. These include some compactifications of symmetric varieties of [D-P2],[D-P3], the compactifications of configuration spaces of [FM], and the compactifications of arrangements of complements of linear subspaces of [D-P1]. See § 4 for these examples.