It is known that there are exactly 95 weighted projective spaces having Gorenstein $K3$ surfaces as anticanonical divisors, some of which have isometric Picard lattices for generic members. For each set of such families, an explicit birational correspondence coming from a torus action is constructed in this paper. As a result the number of `essentially different' families of weighted Gorenstein $K3$ surfaces is 75.
"Isomorphism among Families of Weighted $K3$ Hypersurfaces." Tokyo J. Math. 35 (2) 461 - 467, December 2012. https://doi.org/10.3836/tjm/1358951330