# 1988 Limits of Tangent Spaces

Limits of Tangent Spaces (Donal O'Shea).

The students in O'Shea's group were David Banach (Holy Cross), Sara Billey (MIT), Tessa Cambell (Mount Holyoke) and Constantin Teleman (Harvard). The group developed and implemented algorithms for calculating limits of tangents to hypersurface singularities. These algorithms were based on Groebner basis methods and results of Le and Teissier. They resulted in the first computations of limiting tangent spaces and exceptional lines to simple, unimodal and bimodal surface singularities. In addition, the group was able to recast several equisingularity conditions, notably \mu -constancy and \mu *-constancy, in previously unsuspected algebraic forms which imply, but are not implied by, integral closure conditions.