Meromorphic quotients for some holomorphic G-actions

Daniel Barlet (1)

1 IECL - Institut Élie Cartan de Lorraine

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 $X$.

Mots clés: finite type cycles; Holomorphic G-action; strongly quasi-proper meromorphic quotient; AMS classification Key words Strongly quasi-proper map

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Daniel Barlet. Meromorphic quotients for some holomorphic G-actions. 2015. ⟨hal-01151383⟩