Meromorphic quotients for some holomorphic G-actions

2015/05/26 by Daniel Barlet, Barlet, Daniel
Mathematics · #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV

paper · pdf · doi:10.48550/arxiv.1505.06932

arxiv created 2015/05/26 · arxiv updated 2015/05/27

Abstract

Using mainly tools from [B.13] and [B.15] we give a necessary and sufficient condition in order that a holomorphic action of a connected complex Lie group G on a reduced complex space X admits a strongly quasi-proper meromorphic quotient. We apply this characterization to obtain a result which assert that, when G = K.B with B a closed complex subgroup of G and K a real compact subgroup of G, the existence of a strongly quasi-proper meromorphic quotient for the B-action implies, assuming moreover that there exists a G-invariant Zariski open dense subset in X which is good for the B-action, the existence of a strongly quasi-proper meromorphic quotient for the G-action on X.

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