Mathematical Research Letters

Volume 19 (2012)

Number 6

Completely integrable torus actions on complex manifolds with fixed points

Pages: 1283 – 1295



Hiroaki Ishida (Osaka City University Advanced Mathematical Institute, Osaka, Japan)

Yael Karshon (Department of Mathematics, University of Toronto, Toronto, Ontario, Canada)


We show that if a holomorphic $n$-dimensional compact torus action on a compact connected complex manifold of complex dimension $n$ has a fixed point then the manifold is equivariantly biholomorphic to a smooth toric variety.


torus action, complex manifold, toric manifold

2010 Mathematics Subject Classification

Primary 14M25. Secondary 32M05, 57S25.

Published 18 July 2013