| Résume | Given an algebraic (or complex analytic) variety X, can we find a proper birational (or bimeromorphic) morphism Y -> X preserving the normal crossings locus of X, such that Y has only singularities from an explicit list of normal forms? For example, in dimension 2, we have to admit additional pinch point singularities. I will talk about progress towards the general case; in particular, about a splitting or factorization result that is a relevant multivariate Newton-Puiseux theorem, and about reduction to normal forms based on the combinatorics of circulant matrices. The work is in
collaboration with André Belotto and Ramon Ronzon Lavie. |
