On the global monodromy of a fibration of the Fermat surface of odd degree \(n\)
Let \(M\) be a complex surface and \(B\) a complex curve. A holomorphic map \(f:M\rightarrow B\) is a degeneration map if it is proper, surjective, if there exist finitely many critical values \(s_i\in B\), \(i=1,\ldots ,r\) and if for \(s\neq s_i\) the fibre \(f^{-1}(s)\) is a compact Riemann surface. Fix a base point \(s_0\neq s_i\), \(i=1,\ldots ,r\). The global monodromy of the fibre \(f^{-1}(s_0)\) is a homomorphism \(\rho :\pi _1(B\backslash \{ s_i\},s_0)\rightarrow {\mathcal M}(f^{-1}(s_0))\), where \({\mathcal M}(f^{-1}(s_0))\) is a mapping class group of the fibre \(f^{-1}(s_0)\). The paper investigates the global topological monodromy of a certain fibration of the Fermat surface without using numerical analysis by computer.
scientific article; zbMATH DE number 5950734
scientific article