Smoothings and rational double point adjacencies for cusp singularities

Smoothings of Schemes with Non-isolated Singularities

In this paper we study the deformation and Q-Gorenstein deformation theory of schemes with non-isolated singularities. We obtain obstruction spaces for the existence of deformations and also for local deformations to exist globally. Finally we obtain explicit criteria in order for a pure and reduced scheme of finite type over a field k to have smoothings and Q-Gorenstein smoothings.

Degenerations of elliptic curves and cusp singularities

This paper gives more or less explicit equations for all twodimensional cusp singularities of embedding dimension at least 4. They are closely related to Felix Klein’s equations for universal curves with level n structure. The main technical result is a description of the versal deformation of an n-gon in P. The final section contains the equations for smoothings of simple elliptic singularitie...

The Signature of Smoothings of Higher Dimensional Singularities

Fourier Integral Operators with Cusp Singularities

Explicit resolutions of cubic cusp singularities

Resolutions of cusp singularities are crucial to many techniques in computational number theory, and therefore finding explicit resolutions of these singularities has been the focus of a great deal of research. This paper presents an implementation of a sequence of algorithms leading to explicit resolutions of cusp singularities arising from totally real cubic number fields. As an example, the ...