Renormalization and resolution of singularities

Understand

Since the seminal work of Epstein and Glaser it is well established that perturbative renormalization of ultraviolet divergences in position space amounts to extension of distributions onto diagonals.

• For a general Feynman graph the relevant diagonals form a nontrivial arrangement of linear subspaces.
• One may therefore ask if renormalization becomes simpler if one resolves this arrangement to a normal crossing divisor.
• In this paper we study the extension problem of distributions onto the wonderful models of de Concini and Procesi, which generalize the Fulton-MacPherson compactification of configuration spaces.