Generalized deformations and holomorphic Poisson cohomology of solvmanifolds

TL;DR

This paper investigates the deformation theory of solvmanifolds with complex structures, analyzing their generalized Kuranishi spaces, stability of structures, and computing holomorphic Poisson cohomology explicitly.

Contribution

It provides a detailed description of generalized Kuranishi spaces for solvmanifolds, studies stability of deformations, and offers explicit cochain complexes for cohomology calculations.

Findings

Generalized Kuranishi spaces are explicitly described for certain solvmanifolds.

Stability of left-invariantness under deformation is established.

Explicit finite-dimensional complexes for holomorphic Poisson cohomology are constructed.

Abstract

We describe the generalized Kuranishi spaces of solvmanifolds with left-invariant complex structures. By using such description, we study the stability of left-invariantness of deformed generalized complex structures and smoothness of generalized Kuranishi spaces on certain classes of solvmanifolds. We also give explicit finite dimensional cohcain complexes which computes the holomorphic Poisson cohomology of nilmanifolds and solvmanifolds.