Universität Regensburg

V. G. Berkovich’s Non-Archimedean analytic geometry provides a natural framework to understand the combinatorial aspects in the theory of toric varities and toroidal embeddings. This point of view leads to a conceptual and elementary proof of the following result : if X is an algebraic scheme over a perfect field and if D is the exceptional normal crossing divisor of a resolution of the singularities of X, the homotpy type of the incidence complexe of D is an invariant of X. This is a generalization of a theorem due to D. Stepanov.