K3 surfaces which cover an enriques surface

Abstract

It is well known that all Enriques surfaces have an algebraic K3 surface as a universal cover. Further, all algebraic K3 surfaces form a 19-dimensional moduli space and all Enriques surfaces form a 10-dimensional moduli space. Thus, it is a natural question which K3 surface is a K3-cover of some Enriques surface. For this, Prof. Keum, my master thesis co-advisor, derived the necessary and sufficient condition on the transcendental lattice of the K3 surface which is a K3-cover of some Enriques surface. In this thesis, we determine which K3 surface with Picard number 19 is a K3-cover of some Enriques surface.