On rotation of complex structures

TL;DR

This paper develops a general framework for understanding how complex structures on Riemannian manifolds can be rotated within a family, analyzing the stability of holomorphic bundles under such transformations.

Contribution

It introduces a unified approach to complex structure rotations, including hyperkähler metrics and Spin-rotations, and characterizes rotable holomorphic bundles.

Findings

Identification of conditions for holomorphic bundles to remain stable under complex structure changes

Extension of known rotation concepts to a broader class of Riemannian manifolds

Characterization of polystable holomorphic bundles in the context of complex structure rotations

Abstract

We put in a general framework the situations in which a Riemannian manifold admits a family of compatible complex structures, including hyperkahler metrics and the Spin-rotations of arxiv:1302.2846. We determine the (polystable) holomorphic bundles which are rotable, i.e., they remain holomorphic when we change a complex structure by a different one in the family.