The Story of Reimann’s Moduli Space
The Story of Reimann’s Moduli Space
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雷曼模空间的故事
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
L. Ji
中科院分区：
文献类型：
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作者：
L. Ji
C上的紧黎曼曲面和射影代数曲线是同一类对象的两个实现。他们的模空间最早由Riemann提出，是当代数学和数学物理的中心对象之一。在这篇笔记中，我们通过强调几个点来解释Riemann模空间的诞生和演化，这些点可能不是一般数学家所熟知的，甚至可能是对模空间的复解析几何理论或代数几何理论感兴趣的一些数学家所不知道的。例如，谁是第一个准确地表述模数问题的人？模空间的含义是什么？谁是第一个给黎曼模空间赋予复杂解析和代数簇结构的人？他们为什么要研究这些问题？黎曼的模空间最初是如何使用的？为什么Riemann选择并使用了modi这个词？为什么泰希米勒要研究泰希米勒空间？泰希米勒对黎曼模空间的贡献是什么？泰希米勒的贡献是什么？
Compact Riemann surfaces and projective algebraic curves over C are two realizations of the same class of objects. Their moduli space was first introduced by Riemann and is one of the central objects of the contemporary mathematics and mathematical physics. In this note, we explain the birth and evolution of Riemann’s moduli space by emphasizing several points which might not be so well-known to the general mathematicians and possibly even to some mathematicians who are interested in either complex analytic or algebraic geometric theories of moduli spaces. For example, who was the first to formulate the moduli problem precisely? What is the meaning of moduli spaces? Who was the first to give complex analytic and algebraic variety structures to Riemann’s moduli space? Why did they study these problems? How was Riemann’s moduli space first used? And why did Riemann choose and use the word moduli? Why did Teichmüller study Teichmüller space? What were Teichmüller’s contributions to Riemann’s moduli space? What were Teichmüller’s contributions to