Aut(P^n) has finitely many conjugacy classes of finite subgroups G for which P^n is G-birationally rigid when n≥3, plus a superrigidity theorem for P^4 with G isomorphic to PSp_4(F_3).
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On G-birational rigidity of projective spaces
Aut(P^n) has finitely many conjugacy classes of finite subgroups G for which P^n is G-birationally rigid when n≥3, plus a superrigidity theorem for P^4 with G isomorphic to PSp_4(F_3).