Five embeddings of one simple group

We propose a new method to study birational maps between Fano varieties based on multiplier ideal sheaves. Using this method, we prove equivariant birational rigidity of four Fano threefolds acted on by the group $ \mathrm {A}_6$. As an application, we obtain that $ \mathrm {Bir}(\mathbb{P}^{3})$ has at least five non-conjugate subgroups isomorphic to $ \mathrm {A}_{6}$. - See more at: http://www.ams.org/journals/tran/2014-366-03/S0002-9947-2013-05768-6/home.html#sthash.TuoIlwVG.dpuf