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

TL;DR

This paper generalizes the concept of essential deformations to higher-page $ ext{page-}1$-$ar{ ext{d}}$-manifolds, establishing an unobstructedness theorem and analyzing small deformations of specific solvmanifolds, extending previous results on Iwasawa manifolds.

Contribution

It introduces the notion of essential deformations for page-1-$ar{ ext{d}}$-manifolds and proves an unobstructedness theorem analogous to classical results, expanding deformation theory.

Findings

Established an analogue of the Bogomolov-Tian-Todorov theorem for page-1-$ar{ ext{d}}$-manifolds.

Analyzed small deformations of Nakamura solvmanifolds.

Reinterpreted the Iwasawa manifold and its 5-dimensional analogue within this framework.

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.