Categorical Aspects of the KSB Correspondence I

Explore the categorical aspects of the Kollár–Shepherd-Barron (KSB) correspondence in this comprehensive lecture by Giancarlo Urzua from the Hausdorff Center for Mathematics. Begin with an introduction to M-resolutions of 2-dimensional cyclic quotient singularities and the KSB correspondence. Delve into N-resolutions through Hirzebruch-Jung continued fractions. Discover how N-resolutions can be constructed from M-resolutions using a braid group action induced by the Minimal Model Program (MMP) on degenerations of surfaces. Examine the application of these concepts to Dolgachev surfaces. This talk, based on joint work with Jenia Tevelev, provides a deep dive into the mathematical intricacies of surface singularities and their resolutions over the course of 63 minutes.