Classification of multiplicity free Hamiltonian actions of complex tori on Stein manifolds

Ivan V. Losev

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arXiv · 0706.0632

Classification of multiplicity free Hamiltonian actions of complex tori on Stein manifolds

Ivan V. Losev

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Abstract

A Hamiltonian action of a complex torus on a symplectic complex manifold is said to be {\it multiplicity free} if a general orbit is a lagrangian submanifold. 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-tuple consisting of a Stein manifold $Y$, an étale map $Y\to \t^*$, a set of divisors on $Y$ and elements of $H^2(Y,\Z)^{\oplus n}, H^2(Y,\C)$. We show that $X$ is uniquely determined by this invariants. Furthermore, we describe all 5-tuples arising in this way.

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BibTeX RIS

Ivan V. Losev. 2007-07-12. Classification of multiplicity free Hamiltonian actions of complex tori on Stein manifolds. https://arxiv.org/abs/0706.0632

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