The mixed Hodge structure on the fundamental group of a punctured Riemann surface
The mixed Hodge structure on the fundamental group of a punctured Riemann surface
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刺穿黎曼曲面基本群上的混合 Hodge 结构
DOI：
10.1090/s0002-9939-00-05675-6
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
Rainer H. Kaenders
中科院分区：
文献类型：
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作者：
Rainer H. Kaenders
给定亏格为g的紧致Riemann曲面X和X上的不同点p和q，我们考虑非紧致Riemann曲面X：= X \ {q}，其基点为p ∈ X.研究了与iri（X，p）的前两步相关的混合Hodge结构的扩张.我们证明了它决定了皮科（X）中的元素（2g q 2 p K），其中K表示X的典型因子以及与rn（X，p）相关联的相应扩张.最后，我们推出了一个点Torelli定理穿孔黎曼曲面。
Given a compact Riemann surface X of genus g and distinct points p and q on X, we consider the non-compact Riemann surface X := X \ {q} with basepoint p E X. The extension of mixed Hodge structures associated to the first two steps of iri(X, p) is studied. We show that it determines the element (2g q 2p K) in Pico (X), where K represents the canonical divisor of X as well as the corresponding extension associated to rn (X, p). Finally, we deduce a pointed Torelli theorem for punctured Riemann surfaces.