A structure theorem for fibrations on Delsarte surfaces

Details A structure theorem for fibrations on Delsarte surfaces A structure theorem for fibrations on Delsarte surfaces

2012-04-18

arxiv.org/abs/1204.4103v1

Mathematics

Algebraic Geometry

Scientific paper

In this paper we study a special class of fibrations on Delsarte surfaces. We call these fibrations Delsarte fibrations. We show that after a specific cyclic base change the fibration is the pull back of a fibration with three singular fibers, and that this second base change is completely ramified at two points where the fiber is singular. As a corollary we show that every Delsarte fibration of genus 1 with nonconstant $j$-invariant occurs as the base change of an elliptic surface from Fastenberg's list of rational elliptic surfaces with $\gamma<1$.

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