Seminar Algebra and Geometry: Yves de Cornulier (Lyon 1)

Commensurating actions of birational groups

Given a group G, a G-action on a set D commensurates a subset M if M differs from each of its G-translates by finitely many elements. Commensurating actions naturally induce actions on CAT(0) cube complexes. For every irreducible variety X, we define a set of (virtual) hypersurfaces, which contains the set of hypersurfaces of X and on which the group Bir(X) of birational self-transformations of X acts, extending its partial action on hypersurfaces. This action commensurates the set of hypersurfaces of X. This construction thus provides information about the structure of Bir(X) and its subgroups. (Joint work with Serge Cantat)

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