Curvature and Limits of Normals to Surface Singularities (Donal O'Shea).
The students in O'Shea's 1990 group were Chrissie Beaber (MHC, '91), Eileen Cheng (MHC, '92), Brendan Hassett (Yale, '93), Gwendolyn Lloyd (Bryn Mawr, '91) and Rebecca Runnels (Holy Cross, '91). The group developed a method for computing principal curvatures of algebraic surfaces in complex three-space and used it to compare the asymptotics of principal curvatures along arcs on surfaces approaching a singularity tangent to exceptional lines with arcs approaching transverse to exceptional lines. Their results show a higher order of approach to infinity along arcs tangent to exceptional lines. They were able to use their approach to phrase obstructions to exponential maps in terms of limiting normals.