We prove that a projective vertical exact log smooth morphism of fs log analytic spaces with a base of log rank one yields polarized log Hodge structures in the canonical way.
"Geometric polarized log Hodge structures with a base of log rank one." Kodai Math. J. 43 (1) 57 - 83, March 2020. https://doi.org/10.2996/kmj/1584345688