Katz's middle convolution algorithm
Katz's middle convolution algorithm
复制标题
Katz的中卷积算法
DOI：
10.4310/pamq.2009.v5.n2.a8
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发表时间：
2006
影响因子：
0.7
通讯作者：
C. Simpson
中科院分区：
文献类型：
--
作者：
C. Simpson
这是 Katz 在 ${\bf P}^1-\{ q_1,\ldots , q_n\}$ 上局部系统上的中间卷积运算的说明性说明。我们描述了 Betti 和 de Rham 版本，并指出它们遵循 Volklein、Dettweiler-Reiter、Haraoka-Yokoyama 给出了局部系统的不同模空间之间的同构。 Kostov应用Katz算法的方案是，在中间卷积不再降低秩的范围内，应该给出局部系统的直接构造。科斯托夫和克劳利-博维已经完成了这项工作。我们在这里使用分圆调和丛的概念描述了一种替代结构：这些类似于霍奇结构的变体，只是霍奇分解可以绕一圈。
This is an expository account of Katz's middle convolution operation on local systems over ${\bf P}^1-\{ q_1,\ldots , q_n\}$. We describe the Betti and de Rham versions, and point out that they give isomorphisms between different moduli spaces of local systems, following Volklein, Dettweiler-Reiter, Haraoka-Yokoyama. Kostov's program for applying the Katz algorithm is to say that in the range where middle convolution no longer reduces the rank, one should give a direct construction of local systems. This has been done by Kostov and Crawley-Boevey. We describe here an alternative construction using the notion of cyclotomic harmonic bundles: these are like variations of Hodge structure except that the Hodge decomposition can go around in a circle.