No abstract

We study finite p-subgroups of birational automorphism groups. By virtue of boundedness theorem of Fano varieties, we prove that there exists a constant R(n) such that a rationally connected variety of dimension n over an algebraically closed field is rational if its birational automorphism group contains a p-subgroups of maximal rank for p > R(n). Some related applications on Jordan property are discussed.

No abstract

We prove a structure theorem for the Albanese maps of varieties with Q-linearly trivial log canonical divisors. Our start point is the action of a nonlinear algebraic group on a projective variety.

For a nonsingular projective threefold of general type X over the field of complex numbers, we show that the fourth pluricanonical map ϕ 4 is not birational onto its image if and only if X is birationally fibred by (1, 2)-surfaces, provided that vol(X ) 30 3 . We also have similar characterization of birationality of ϕ 3 .