The fibration is one of the fundamental methods in the study of algebraic surfaces. In the early years, fibration was studied by using the method of complete classification of singular fibres, which was obtained throu...The fibration is one of the fundamental methods in the study of algebraic surfaces. In the early years, fibration was studied by using the method of complete classification of singular fibres, which was obtained through studying the combinatorical properties of singular fibres. But with the rising of the genus of fibration, this method will not work now. In 1977, a more essential classification of singular fibres of genus two was given by Eiji Horikawa by using relative canonical maps. Prof. Xiao Gang has successfully improved the classification of Horikawa and effectively studied some algebra.ic surfaces by using his classification. We know that, ordinarily, through the classification of singular fibres, parameters of fibration can be obtained. Based on this, we study the properties of surfaces. But for some parameters, we can effectively describe them only by the study of combinatorical properties and topological展开更多
文摘The fibration is one of the fundamental methods in the study of algebraic surfaces. In the early years, fibration was studied by using the method of complete classification of singular fibres, which was obtained through studying the combinatorical properties of singular fibres. But with the rising of the genus of fibration, this method will not work now. In 1977, a more essential classification of singular fibres of genus two was given by Eiji Horikawa by using relative canonical maps. Prof. Xiao Gang has successfully improved the classification of Horikawa and effectively studied some algebra.ic surfaces by using his classification. We know that, ordinarily, through the classification of singular fibres, parameters of fibration can be obtained. Based on this, we study the properties of surfaces. But for some parameters, we can effectively describe them only by the study of combinatorical properties and topological