Deformations of higher-page analogues of ¿¿¯-manifolds

We extend the notion of small essential deformations of Calabi–Yau complex structures from the case of the Iwasawa manifold, for which they were introduced recently by the first-named author, to the general case of page-1-¿¿¯ -manifolds that were jointly introduced very recently by all three authors. We go on to obtain an analogue of the unobstructedness theorem of Bogomolov, Tian and Todorov for Calabi–Yau page-1-¿¿¯ -manifolds. As applications of this discussion, we study the small deformations of certain Nakamura solvmanifolds and reinterpret the cases of the Iwasawa manifold and its 5-dimensional analogue from this standpoint