Irreducibility and monodromy of some families of linear series
Irreducibility and monodromy of some families of linear series
复制标题
某些线性级数族的不可约性和单性
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
J. Harris
中科院分区：
文献类型：
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作者：
D. Eisenbud;J. Harris
- 设g，r，d是正整数，使得g=（r-{-1）（g-d-\-r），使得亏格g的一般曲线只有n个g^s.本文将证明，对于适当的曲线族^ -> B，在^ -> B的所有纤维上的所有cff族是不可约的。我们通过分析纤维上97的集合上的单值作用来做到这一点，使用退化到可约曲线和我们的极限级数技术[198？^]。在r = 1的情况下，我们证明了更尖锐的声明，monodromy是充分的对称群，一个结果的动机由一个问题所提出的Verdier，并适用于他的研究调和映射从2到S（Verdier [198？]）。如果我们取^为模空间My的适当开集B上的泛曲线，则c^的族是B的有限覆盖，并且通过本文开发的工具分析的该覆盖的分支轨迹（在r=l的情况下）在我们的证明中的偶亏格情况下起着基本作用[198？^]该夹具具有用于所有g 24通用类型。
— Let g, r, and d be positive integers such that g=(r-{-1) (g—d-\-r), so that the general curve of genus g has only finitely many g^s. We will show in this paper that for suitable families of curves ^ -> B, the family of all cffs on all fibers of ^ -> B is irreducible. We do this by analyzing the monodromy action on the set of 97 on a fibre, using a degeneration to reducible curves and our technique of limit series [198?^]. In the case r = 1 we prove the sharper statement that the monodromy is the full symmetric group, a result motivated by a problem posed by Verdier, and applied by him in the study of harmonic maps from 2 to S (Verdier [198?]). If we take ^ to be the universal curve over a suitable open set B of the moduli space My then the family of c^'s is a finite cover of B, and the branch locus of this cover (in the case r=l), analyzed through the tools developed in this paper, plays a fundamental role in the even-genus case in our proof [198?^] that Jig has general type for all g 24.