Moment polytopes in real symplectic geometry I

Paul-Emile Paradan (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

Let Z be the real part of a Kähler Hamiltonian manifold M. The O'Shea-Sjamaar's Theorem tells us that the moment polytope Delta(Z) corresponds to the anti-invariant part of the Kirwan polytope Delta(M). The purpose of the present paper is to explain how to parameterize the equations of the facets of Delta(Z) in terms of real Ressayre's pairs of Z.

Mots clés: moment polytope; group action; stratification; real structure of complex manifold

Domaines: Géométrie symplectique [math.SG]; Géométrie différentielle [math.DG]

Paul-Emile Paradan. Moment polytopes in real symplectic geometry I. 2020. ⟨hal-03065807⟩