Higher Chow cycles on K3 surfaces attached to plane quartics

In this paper, we give an explicit construction of higher Chow cycles of type (2, 1) on K3 surfaces obtained as quadruple coverings of the projective plane ramified along smooth quartics. The construction uses a pair of bitangents of the quartics. We prove that the higher Chow cycles generate a rank 2 subgroup in the indecomposable part of the higher Chow group for very general members, by using a specialization argument and an explicit computation of the regulator map.