K3 surfaces associated to curves of genus two

Details K3 surfaces associated to curves of genus two K3 surfaces associated to curves of genus two

2007-01-24

arxiv.org/abs/math/0701669v1

Int. Math. Res. Not. (IMRN) 2008, no. 6: Art. ID rnm165, 26 pp

Mathematics

Algebraic Geometry

22 pages, 4 figures

Scientific paper

10.1093/imrn/rnm165

It is known (work of Galluzzi,Lombardo,Dolgachev and Naruki) that there is a unique K3 surface X which corresponds to a genus 2 curve C such that X has a Shioda-Inose structure with quotient birational to the Kummer surface of the Jacobian of C. In this paper we give an explicit realization of X as an elliptic surface over P^1 with specified singular fibers of type II^* and III^*. We describe how the Weierstrass coefficients are related to the Igusa-Clebsch invariants of C.

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