On the normality of the null-fiber of the moment map for θ- and tori representations.

Let ( G , V ) be a representation with either G a torus or ( G , V ) a locally free stable θ -representation. We study the fiber at 0 of the associated moment map, which is a commuting variety in the latter case. We characterize the cases where this fiber is normal. The quotient ( i.e. the symplectic reduction) turns out to be a specific orbifold when the representation is polar. In the torus case, this confirms a conjecture stated by C. Lehn, M. Lehn, R. Terpereau and the author in a former article. In the θ -case, the conjecture was already known but this approach yield another proof. [ABSTRACT FROM AUTHOR]