Arcs and resolution of singularities

Arcs and Resolution of Singularities

For a certain class of varieties X, we derive a formula for the valuation dX on the arc space L(Y ) of a smooth ambient space Y , in terms of an embedded resolution of singularities. A simple transformation rule yields a formula for the geometric Poincaré series. Furthermore, we prove that for this class of varieties, the arithmetic and the geometric Poincaré series coincide. We also study the ...

Renormalization and Resolution of Singularities

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...

Alterations and resolution of singularities

Resolution of Cosmological Singularities

We show that a class of 3+1 dimensional Friedmann-RobertsonWalker cosmologies can be embedded within a variety of solutions of string theory. In some realizations the apparent singularities associated with the big bang or big crunch are resolved at non-singular horizons of higher-dimensional quasi-black hole solutions (with compactified real time); in others plausibly they are resolved at D-bra...

Crepant Resolution of Trihedral Singularities

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