Abstract:
A birational automorphism f of an algebraic variety X is an algebraic isomorphism of one Zariski open subset of X to another open subset. A natural question arises: is there a birational model of X where f induces a regular automorphism. This question is related to the invariants of the inverse image action of f on the singular cohomology groups of X. I am going to talk about this relation with an example of a birational automorphism of a three dimensional projective space which preserves a cubic surface pointwise.