Seminar Algebra and Geometry: Pascal Fong (Leibniz Universität Hannover)

Isotrivial elliptic surfaces

Recently, Brion introduced and developed the theory of equivariantly normal curves. These curves arise naturally in the study of smooth projective surfaces equipped with a faithful action of an elliptic curve. We will see that such a surface is isomorphic to a contracted product E\times^G X, where E is an elliptic curve, G is a finite subgroup scheme of E and X is a G-normal curve. In this talk, we study this family of surfaces, which contains the classical example of quasi-hyperelliptic surfaces given by Bombieri and Mumford.

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