Junior Geometry Seminar – Marc Truter (Warwick)

Abstract: Fano’s are one of the main objects of study in the Minimal Model Program, an algorithm used to classify varieties. In dimensions 1 and 2 the classification of Fano’s is complete, and despite the fact Fano 3-folds have been studied for nearly a century, their classification is still to be fully solved. Some important cases have, however, been completed. For example, we have 105 smooth Fano 3-folds and 95 Fano 3-fold hypersurface families. For 4-folds very little is known. There has been some recent progress; in 2016, Fano 4-fold hypersurfaces with a condition known as quasismooth were classified into 11,617 families. My project looks at studying the other nastier and more prominent half, the nonquasismooth case, using computational methods.