ON RESOLVING SINGULARITIES

Resolving Gravitational Singularities

We review recent progress on the resolution of gravitational singularities in string theory. The main example is the fundamental string in five dimensions which is singular in the standard supergravity description but regular after taking into account higher derivative corrections determined by anomalies and supersymmetry. The application of the AdS/CFT correspondence to geometries that require...

Resolving Singularities in (0,2) Models

In contrast to the familiar (2, 2) case, the singularities which arise in the (0, 2) setting can be associated with degeneration of the base Calabi–Yau manifold and/or with degenerations of the gauge bundle. We study a variety of such singularities and give a procedure for resolving those which can be cured perturbatively. Among the novel features which emerge are models in which smoothing sing...

Resolving Singularities with Cartan’s Prolongation

Resolving 3-dimensional toric singularities

This paper surveys, in the first place, some basic facts from the classification theory of normal complex singularities, including details for the low dimensions 2 and 3. Next, it describes how the toric singularities are located within the class of rational singularities, and recalls their main properties. Finally, it focuses, in particular, on a toric version of Reid’s desingularization strat...

Resolving Singularities of Plane Analytic Branches with One Toric Morphism

Let (C; 0) be an irreducible germ of complex plane curve. Let ? N be the semigroup associated to it and C ? C g+1 the corresponding monomial curve, where g is the number of Puiseux exponents of (C; 0). We show, using the specialization of (C;0) to (C ? ; 0), that the same toric morphisms