The fundamental group of the complement of the branch curve of ℂℙ1 × T |
| |
基金项目: | The third author is partially supported by DAAD and EU-network HPRN-CT-2009-00099(EAGER); The Emmy Noether Research Institute for Mathematics and the Minerva Foundation of Germany; The Israel Science Foundation grant # 8008/02-3 (Excellency Center "Group Theoretic Methods in the Study of Algebraic Varieties"). |
| |
摘 要: | Denoting by T the complex projective torus, we can embed the surface CP^1 × T in CP^5. In this paper we compute the fundamental group of the complement of the branch curve of this surface. Since the embedding is not "ample enough", the embedded surface does not belong to the classes of surfaces where the fundamental group is virtually solvable: a property which holds for these groups for "ample enough" embeddings. On the other hand, as it is the first example of this computation for non simply-connected surfaces, the structure of this group (as shown in this paper) give rise to the extension of the conjecture regarding the structure of those fundamental groups of any surface.
|
关 键 词: | 曲线曲面 物质表面 CP 群体结构 嵌入式 延伸表面 基本群 单连通 |
本文献已被 维普 SpringerLink 等数据库收录! |