Fundamental groups of elliptic fibrations and the invariance of the plurigenera for surfaces with odd first Betti number
In the paper under review, the author studies the fundamental group of an elliptic surface and the close relationship between the Kodaira dimension of an elliptic surface with odd first Betti number and the geometry of its base orbifold. It is proved that every elliptic fibration \(X \to C\) with trivial first direct image sheaf can be obtained from a product \(C \times E\), where \(E\) is an elliptic curve, by means of logarithmic transformations. The fundamental groups of such an elliptic fibration is computed. In addition, the author presents a new and much shorter proof to the fact that the plurigenera and hence the Kodaira dimension of a complex surface with odd first Betti number are determined by the isomorphism type of the fundamental group.
scientific article; zbMATH DE number 2175359