Quaternionic LVM Manifolds

We study a quaternionic counterpart of the quotient construction underlying LVM manifolds. From an admissible configuration \[ Λ=(λ_1,\ldots,λ_n)\subset{\mathbb H}^m\simeq{\mathbb R}r^{4m}, \qquad n>4m, \] we obtain a smooth compact intersection of real quadrics $Z_{\mathbb H}(Λ)\subset{\mathbb H}^n