A spherical variety is a normal variety $ X$ together with an action of a connected reductive affine algebraic group $ G$ , a Borel subgroup $ B\subset G$ , and a base point $ x_0\in X$ such that the $ B$ -orbit of $ x_0$ in $ X$ is a dense open subset of $ X$ .

A wonderful variety is a smooth complete variety $ X$ with the action of a semisimple simply connected group $ G$ such that there is a point $ x_0\in X$ with open $ G$ orbit and such that the complement $ X\setminus G\cdot x_0$ is a union of prime divisors $ E_1,\cdots, E_t$ having simple normal crossing, and such that the closures of the $ G$ -orbits in $ X$ are the intersections $ \bigcap_{i\in I}E_i$ where $ I$ is a subset of $ \{1,\dots, t\}$ .

Now, fix a connected reductive affine algebraic group $ G$ and a Borel subgroup $ B\subset G$ . Could there exist two non isomorphic smooth complete varieties that are spherical with respect to $ (G,B)$ and wonderful with respect to $ G$ ?