Singularities and group actions

Singularities and Group Actions

Moving Frames and Singularities of Prolonged Group Actions

The prolongation of a transformation group to jet bundles forms the geometric foundation underlying Lie’s theory of symmetry groups of differential equations, the theory of differential invariants, and the Cartan theory of moving frames. Recent developments in the moving frame theory have necessitated a detailed understanding of the geometry of prolonged transformation groups. This paper begins...

Mixed Braid Group Actions from Deformations of Surface Singularities

We consider a set of toric Calabi–Yau varieties which arise as deformations of the small resolutions of type A surface singularities. By careful analysis of the heuristics of B-brane transport in the associated GLSMs, we predict the existence of a mixed braid group action on the derived category of each variety, and then prove that this action does indeed exist. This generalizes the braid group...

Effective Actions near Singularities

We study the heterotic string compactified on K3× T 2 near the line T = U , where the effective action becomes singular due to an SU(2) gauge symmetry enhancement. By ‘integrating in’ the light W± vector multiplets we derive a quantum corrected effective action which is manifestly SU(2) invariant and non-singular. This effective action is found to be consistent with a residual SL(2,Z) quantum s...

Normal singularities with torus actions

We propose a method to compute a desingularization of a normal affine variety X endowed with a torus action in terms of a combinatorial description of such a variety due to Altmann and Hausen. This desingularization allows us to study the structure of the singularities of X. In particular, we give criteria for X to have only rational, (Q-)factorial, or (Q-)Gorenstein singularities. We also give...