Converting virtual link diagrams to normal ones

A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative. In this paper, we introduce a method of converting a virtual link diagram to a normal virtual link diagram by use of the double covering technique. We show that the normal virtual link diagrams obtained by this method from two equivalent virtual link diagrams are related by generalized Reidemeister moves and Kauffman flypes.