Birational self-maps and piecewise algebraic geometry

Stéphane Lamy (1) , Julien Sebag (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IRMAR - Institut de Recherche Mathématique de Rennes

Let X be a smooth projective complex variety, of dimension 3, whose Hodge numbers h^{3,0}(X), h^{1,0}(X) both vanish. Let f: X--> X be a birational map that induces an isomorphism on (dense) open subvarieties U,V of X. Then we show that the complex reduced varieties (X \ U), (X \ V) are piecewise isomorphic.

Mots clés: birational map; piecewise isomorphism

Domaines: Géométrie algébrique [math.AG]

Stéphane Lamy, Julien Sebag. Birational self-maps and piecewise algebraic geometry. Journal of Mathematical Sciences the University of Tokyo, 2012, 19 (3), pp.325-357. ⟨hal-00654982⟩