Minimal Splitting Surface Determined by a Projection of a Smooth Quartic Surface

摘要

Let S be a smooth quartic hypersurface in the projective three space and consider a projection of S from P ∈ S to a hyperplane H. This projection induces an extension of fields k(S)/k(H). Let LP be the Galois closure and X a smooth model of Lp. We show that X is a surface of general type if the extension is not GMois.