Non-symplectic actions on complex projective spaces

TL;DR

This paper constructs smooth actions of any compact Lie group on complex projective spaces that do not preserve any symplectic structure, highlighting new possibilities for group actions in symplectic geometry.

Contribution

It introduces a method to create smooth group actions on complex projective spaces that are inherently non-symplectic, expanding understanding of symmetry in complex geometry.

Findings

Existence of smooth non-symplectic actions for all compact Lie groups

Construction techniques for such actions on complex projective spaces

Implications for symplectic and complex geometry

Abstract

We construct smooth actions of arbitrary compact Lie groups on complex projective spaces, such that the corresponding transformations arising from the group action do not preserve any symplectic structure on the complex projective space.