Stable branch curves and braid monodromies
Stable branch curves and braid monodromies
复制标题
稳定的分支曲线和辫状单峰
DOI：
10.1007/bfb0090891
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发表时间：
1981
期刊：
影响因子：
--
通讯作者：
B. Moishezon
中科院分区：
文献类型：
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作者：
B. Moishezon
在代数曲面的分类中，有一类被称为“一般型曲面”。这简单地反映了其他曲面是特殊的（直纹、椭圆、阿贝尔或K3）的事实。不幸的是，对一般类型的表面的分类知之甚少。它们在l维情况下的类似物是亏格> 1的曲线，其中分类由两个主要事实给出：1）亏格的任何值2）给定亏格的曲线的模空间是连通的（实际上是不可约的）并且具有（复）维数3g-3。这两个事实都可以通过研究所谓的”稳定黎曼曲面”的结构得到，1我们指的是稳定的有限态射g：X（X是连通的l维复流形）。对于任何这样的态射，用M '表示X的所有点的集合，其中g不为埃塔尔，并用M= g（M'）表示。设n= deg g。存在自然满射1 s：rr 1-M，.）Sn（n次对称群），称为“g的单值性”。关于这种monodromies的一个重要事实是关于存在”monodromy的标准形式”的经典定理，该工作已部分得到国家科学院的支持。
In the classification of algebraic surfaces one of the classes is called" surfaces of general type",. which simply reflects the fact that other surfaces are special (ruled, elliptic, abelian or K3). Unfortunately, not much is known about the classification of surfaces of general type. Their analog in l-dimensional case are curves of genus> 1, where classification is given by two main facts: 1) any value of genus 2) the moduli space of curves of given genus is connected (actually irreducible) and has (complex) dimension 3g-3. Both these facts could be obtained by studying constructions of the so called" stable Riemann surface", 1 by which we mean stable finite morphisms g: X(X is a connected l-dimensional complex manifold). For any such morphism denote by M'the set of all points of X where g is not etal and by M= g (M'). Let n= deg g. There is a natural surjection 1 s: rr l-M,.) Sn (symmetric group of degree n), which is called" the monodromy of g". An important fact about such monodromies is a classical theorem about existance of a" normal form for monodromy" which This work has been partially supported by the National Science