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We study the moduli space ${\cal M}$ of N=(4,4) superconformal field theorieswith central charge c=6. After a slight emendation of its global description wefind the locations of various known models in the component of ${\cal M}$associated to K3 surfaces. Among them are the Z_2 and Z_4 orbifold theoriesobtained from the torus component of ${\cal M}$. Here, SO(4,4) triality isfound to play a dominant role. We obtain the B-field values in direction of theexceptional divisors which arise from orbifolding. We prove T-duality for theZ_2 orbifolds and use it to derive the form of ${\cal M}$ purely withinconformal field theory. For the Gepner model (2)^4 and some of its orbifolds wefind the locations in ${\cal M}$ and prove isomorphisms to nonlinear sigmamodels. In particular we prove that the Gepner model (2)^4 has a geometricinterpretation with Fermat quartic target space.Comment: 58 pages, version submitted to Comm. Math. Phys; references added and  minor mistakes correcte

A Hiker's Guide to K3.¶Aspects of N= (4,4) Superconformal Field Theory¶with Central Charge c= 6