Degenerations of del Pezzo Surfaces with Only Wahl Singularities

Explore the classification of degenerations of del Pezzo surfaces with only Wahl singularities in this advanced mathematics lecture. Learn about complex nonsingular del Pezzo surfaces and their degenerations with log-terminal singularities, specifically focusing on Wahl singularities which are log-terminal singularities that admit rational homology smoothing with Milnor number equal to zero. Discover how this classification extends existing knowledge about the complex projective plane through Markov numbers, and examine practical applications of these theoretical results. The presentation covers joint research work with Juan Pablo Zúñiga from UC Chile, offering insights into cutting-edge developments in algebraic geometry and singularity theory. This lecture was delivered as part of the "New Developments in Singularity Theory" conference, a joint IMSA & ICMS event supported by the Simons Foundation, National Science Foundation, and the University of Miami.