UC Santa Barbara

This dissertation presents a number of results on the partial compactification of the Bridgeland stability manifolds associated to a few well-behaved complex varieties by considering their embedding in a certain real projective space. The first main result demonstrates that encoding stability conditions by the masses of a large set of objects always yields an embedding for a significant number of geometric examples — in almost all cases, however, this yields an embedding into an infinite-dimensional space. The second main result shows that a large class of geometric examples proposed by fail to admit a Thurston compactification. The last result is a description of the boundary of the compactification for a certain non-compact Calabi-Yau surface; this can be seen as a geometric realization of the original Thurston compactification for the A2-quiver introduced by Bapat, Deopurkar, and Licata. This leads to a similar approach in one dimension higher with a much more complicated boundary structure.