Smoothing Toroidal Crossing Fano Varieties Using Log Structures

Watch a 71-minute lecture exploring the construction of generically log smooth Fano varieties from reflexive polytopes, presented by Helge Ruddat from the University of Stavanger. Delve into joint research with Alessio Corti that examines how log structures derived from zero-mutable Laurent polynomials can be used for smoothing and resolving toroidal crossing Fano varieties. Learn about conjectures regarding the smoothability of these log structures and their relationship to toric singularities, as proposed by Corti-Filip-Petracci. Examine ongoing work with Tim Gräfnitz on proving these conjectures for admissible log singularities and Tom and Jerry singularities. Understand how this research program aims to develop a unified construction method for compact Fano manifolds, with particular emphasis on Fano 3-folds and potential applications to Q-Gorenstein Fano varieties.