Explicit resolution of local singularities of moduli-spaces.
Explicit resolution of local singularities of moduli-spaces.
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模空间局部奇点的显式解析。
DOI：
10.1515/crll.1997.483.183
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
G. Faltings
中科院分区：
文献类型：
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作者：
G. Faltings
本文对模问题中出现的某些类型的奇点给出了一种新的处理方法。Chai和Norman首先研究了这些，Deligne和Pappas进行了一些改进（见[CN]，[DP]）。主要的结果是，这些奇点是科恩-麦考利，这是使用显式基（通过杨表）和代数理论与矫直法律。这里我们想证明奇点是有理的这一更强的结果，我们使用G。Kempf分解法（[K]）。而不是组合，我们使用理论的线丛旗品种和紧化的对称空间，特别是事实，这些是弗罗贝尼乌斯分裂。这给出了一个统一的方法，适用于（或应该适用于）所有半单代数群。应该指出的是，类似的发展发生在理论的舒伯特品种，其中明确的基础（为经典集团）已取代更统一和一般的论点。我们研究的奇异性的基本类型是两个n维矩阵B和C满足B C = C B = p的奇异性（例如这些出现在[F]中）。对于其它经典群，我们还假设C = B* 是（对称或辛）内积的伴随，或者B = 5，C = C。
In this paper we give a new approach to certain types of singularities which appear in moduli-problems. These have been first studied by Chai and Norman, with some improvements by Deligne and Pappas (see [CN], [DP]). The main result is that these singularities are Cohen-Macaulay, which is shown using explicit bases (via Young-tableaux) and the theory of algebras with straightening law. Here we want to show the stronger result that the singularities are rational, and we use G. Kempf's method of resolution ([K]). Instead of combinatorics we use the theory of line-bundles on flag-varieties and compactifications of Symmetrie spaces, and especially the fact that these are Frobenius-split. This gives a unified approach which works (or should work) for all semisimple algebraic groups. It should be remarked that a similar development occured in the theory of Schubert-varieties, where explicit bases (for the classical groups) have been replaced by more uniform and general arguments. The basic type of singularity we study is that of two n w-matrices B and C satisfying B C = C B = p (for example these appear in [F]). For the other classical groups we assume in addition that C = B* is the adjoint for a (Symmetrie or symplectic) inner product, or that B = 5, C = C.