Split Nakamura manifolds and their automorphisms

TL;DR

This paper investigates split Nakamura manifolds, focusing on their cohomological properties, deformation behavior, and automorphism groups, extending Nakamura's original threefold to higher dimensions.

Contribution

It introduces the class of split Nakamura manifolds, analyzes their cohomology, spectral sequence degeneration, and automorphism groups, providing new insights into their geometric structure.

Findings

De Rham and Dolbeault cohomology computed for these manifolds.

Conditions for Fr"olicher spectral sequence degeneration identified.

Automorphism groups explicitly described.

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 $\mathbb{C}^n \rtimes_\rho \mathbb{C}$ by a lattice. We discuss their de Rham and Dolbeault cohomology, with emphasis on the degeneration of the Fr\"olicher spectral sequence and the $\partial\bar{\partial}$-Lemma, and their deformations. Finally, we describe their automorphism group in detail.