On superconformal field theories associated to very attractive quartics

We study N = (4,4) superconformal field theories with left and right central charge c = 6 which allow geometric interpretations on specific quartic hypersurfaces in CP3. Namely, we recall the proof that the Gepner model (2)(4) admits a geometric interpretation on the Fermat quartic and give an independent crosscheck of this result, providing a link to the "mirror moonshine phenomenon" on K3. We clarify the role of Shioda-Inose structures in our proof and thereby generalize it: We introduce VERY ATTRACTIVE QUARTICS and show how on each of them a superconformal field theory can be constructed explicitly