Deformations of Higher-Page Analogues of $\partial \bar{\partial }$-Manifolds

Abstract

We extend the notion of essential deformations from the case of the Iwasawa manifold, for which they were introduced recently by the first-named author, to the general case of page-$1$-$\partial \bar{\partial }$-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 page-$1$-$\partial \bar{\partial }$-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.

arXiv comment26 pages. Originally part of arXiv:2001.02313, v2: added more background information, Rem. 4.5 and discussion of Nakamura solvmanifolds in §5. Final version. To appear in Math. Z