ON INTERSECTIONS OF QUADRICS
ON INTERSECTIONS OF QUADRICS
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关于二次曲线的交点
DOI：
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发表时间：
1975
期刊：
影响因子：
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通讯作者：
A. Tyurin
中科院分区：
文献类型：
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作者：
A. Tyurin
本文献给作者伊戈尔·罗斯蒂斯拉沃维奇·沙法雷维奇50岁生日，以及他被伦敦数学学会选为荣誉会员。本文转载了作者1973年冬季学期在莫斯科国立大学数学系的一次讲座。这些讲座致力于综述与各种结构的模空间的周期映射有关的几何结果。虽然这个问题是最近才出现的，但它已经有两个重要的问题值得称道：Lefschetz问题和三次三重问题。周期映射论分为局部理论和整体理论。局部理论描述了专制群体对周期的作用；它一直是许多西方文章的主题，因为它提供了一种对韦尔黎曼假说证明中的维度进行归纳的方法。整体理论更多的是几何性质的，但在第一次取得相当大的成功之后(三次三次折叠和曲面K3的问题)，就没有更多的出版物专门研究它了。这篇文章的目的是通过一个相当简单的新例子向读者介绍全球理论。
This article is dedicated to Igor Rostislavovich Shafarevich, on his fiftieth birthday by the author, and on his election as an Honorary Member by the London Mathematical Society. This article reproduces a course of lectures given by the author in the winter semester of 1973 in the Mathematics Faculty of the Moscow State University. The lectures were devoted to a survey of the geometrical results connected with the period mapping of the moduli spaces of various structures. Although this subject has arisen fairly recently, it has already two important problems to its credit: the Lefschetz problem, and the problem of the cubic 3-fold. The theory of the period map is divided up into a local and a global theory. The local theory describes the action of the monodromy group on the periods; it has been the subject of numerous Western articles, since it gives a way of carrying out an induction on the dimension in the proof of the Weil Riemann hypothesis. The global theory is more geometrical, but after the first considerable success (the problem of the cubic 3-fold and of surfaces K3) there have been no more publications devoted to it. The purpose of the present article is to introduce the reader to the global theory by means of a fairly simple new example.