English

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

Algebraic Geometry 2021-07-15 v2 Complex Variables Differential Geometry

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-11-ˉ\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-11-ˉ\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 55-dimensional analogue from this standpoint.

Keywords

Cite

@article{arxiv.2007.15762,
  title  = {Deformations of Higher-Page Analogues of $\partial\bar\partial$-Manifolds},
  author = {Dan Popovici and Jonas Stelzig and Luis Ugarte},
  journal= {arXiv preprint arXiv:2007.15762},
  year   = {2021}
}

Comments

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