Split Nakamura manifolds and their automorphisms

Abstract

In this paper we study the class of \emph{split Nakamura manifolds}, which are a type of solvmanifolds generalizing Nakamura's threefold, defined as quotients of the semidirect product ${\mathbb{C}}^n{⋊}_{\ddot{I}}\mathbb{C}$ by a lattice. We discuss their de Rham and Dolbeault cohomology, with emphasis on the degeneration of the Frölicher spectral sequence and the $\partial \bar{\partial }$-Lemma, and their deformations. Finally, we describe their automorphism group in detail.

19 pages. Comments are welcome!