In mathematics, **Delzant's theorem**, introduced by Thomas Delzant (1988), classifies effective Hamiltonian actions of a torus on a compact connected symplectic manifold of twice the dimension by their image under the momentum mapping (Delzant polytope). A Delzant polytope is a convex polytope in **R**^{n} such that the slopes of the edges of each vertex are given by a basis of **Z**^{n}.

As a corollary, these symplectic manifolds have a complex structure and can be promoted as toric varieties, with invariant Kähler structures.

## References

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