Tsuchihashi's cusp singularities are Buchsbaum 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 ...

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...

Hele - Shaw Flow Near Cusp Singularities

This thesis discusses the radial version of the Hele-Shaw problem. Different from the channel version, traveling-wave solutions do not exist in this version. Under algebraic potentials, in the case that the droplets expand, in finite time, cusps will appear on the boundary and classical solutions may not exist afterwards. Physicists have suggested that for (2p+ 1, 2)-cusps, that near cusp singu...

Rings of Singularities

This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...