Equivariant deformations of the affine multicone over a flag variety
  We prove that the invariant Hilbert scheme parametrising the equivariant deformations of the affine multicone over a flag variety is, under certain hypotheses, an affine space. The proof is based on the construction of a wonderful variety in a fixed multiprojective space. 
Paolo Bravi, Stephanie Cupit-Foutou