Classification of multiplicity free Hamiltonian actions of complex tori on Stein manifolds - Mathematics > Symplectic Geometry

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Abstract: A Hamiltonian action of a complex torus on a symplectic complex manifold issaid to be {\it multiplicity free} if a general orbit is a lagrangiansubmanifold. To any multiplicity free Hamiltonian action of a complex torus$T\cong \C^\times^n$ on a Stein manifold $X$ we assign a certain 5-tupleconsisting of a Stein manifold $Y$, an \-{e}tale map $Y\to \t^*$, a set ofdivisors on $Y$ and elements of $H^2Y,\Z^{\oplus n}, H^2Y,\C$. We show that$X$ is uniquely determined by this invariants. Furthermore, we describe all5-tuples arising in this way.

Autor: Ivan V. Losev

Fuente: https://arxiv.org/