  We formulate the problem of renormalization of Feynman integrals and its
relation to periods of motives in configuration space instead of momentum
space. The algebro-geometric setting is provided by the wonderful
compactifications of arrangements of subvarieties associated to the subgraphs
of a Feynman graph and a (quasi)projective variety. The motive and the class in
the Grothendieck ring are computed explicitly for these wonderful
compactifications, in terms of the motive of the variety and the combinatorics
of the Feynman graph, using recent results of Li Li. The pullback to the
wonderful compactification of the form defined by the unrenormalized Feynman
amplitude has singularities along a hypersurface, whose real locus is contained
in the exceptional divisors of the iterated blowup that gives the wonderful
compactification. A regularization of the Feynman integrals can be obtained by
modifying the cycle of integration, by replacing the divergent locus with a
Leray coboundary. The ambiguities are then defined by Poincare' residues. While
these residues give mixed Tate periods associated to the cohomology of the
exceptional divisors and their intersections, the regularized integrals give
rise to periods of the hypersurface complement in the wonderful
compactification, which can be motivically more complicated.
