As known to all,it is quite difficult to compute the fundamental group of a surface of general type.In this paper,applying Moishezon-Teicher’s algorithm,we investigate the fundamental group of a special surface of ge...As known to all,it is quite difficult to compute the fundamental group of a surface of general type.In this paper,applying Moishezon-Teicher’s algorithm,we investigate the fundamental group of a special surface of general type with zero topological index,namely,the Galois cover of the(2,3)-embedding of CP^1×T.Because the full presentation of the group is very complicated,we compute its special quotient and get an interesting result about its structure.展开更多
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 ...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.展开更多
基金Supported by the ISF-NSFC joint research program(Grant No.2452/17)NSF of China,MST of China(Grant No.2018AAA0101001)STC of Shanghai(Grant No.18dz2271000)。
文摘As known to all,it is quite difficult to compute the fundamental group of a surface of general type.In this paper,applying Moishezon-Teicher’s algorithm,we investigate the fundamental group of a special surface of general type with zero topological index,namely,the Galois cover of the(2,3)-embedding of CP^1×T.Because the full presentation of the group is very complicated,we compute its special quotient and get an interesting result about its structure.
基金supported by DAADEU-network HPRN-CT-2009-00099(EAGER)+2 种基金The Emmy Noether Research Institute for Mathematicsthe Minerva Foundation of GermanyThe Israel Science Foun dation grant #8008/02-3 (Excellency Center "Group Theoretic Methods in the Study of Algebraic Varieties")
文摘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.
