We provide explicit generators of the torsion of the second cohomology of bielliptic surfaces, and we use this to study the pullback map between the Brauer group of a bielliptic surface and that of its canonical cover.
We prove that a smooth projective surface S over an algebraically closed field of characteristic p > 3 is birational to an abelian surface if P1(S) = P4(S) = 1 and h 1 (S, OS) = 2.
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