Singular Fano 4-folds

Lead Research Organisation: University of Warwick
Department Name: Mathematics


Fano 3-folds have been studied for nearly a century, with the 1 and 2 dimensional cases being solved in the 19th century. There is no classification for Fano 3-folds, however it is known that they can be sorted into only finitely many deformation families. Notably, for some of the important classes classifications have been achieved. In particular, the "famous 95", the families whose general member is embedded pluri-anticanonically as a hypersurface.
Birkar's celebrated theorem on the boundedness of Fano varieties proved that in any dimension, with very general hypotheses on the possible singularities, there are only finitely many deformation families for Fano varieties. Working with the terminal singularities of the standard minimal model program, we can ask to enumerate certain subclasses. In 4 dimensions, hypersurfaces that are quasismooth were classified in 2016. Unlike in 3 dimensions, however, there is no q-smoothing result for 4-folds, and the quasismooth case is not expected to account for the majority of hypersurfaces. The project will enumerate terminal Fano 4-folds that are not quasismooth giving the first indication of the weakness of the quasismooth assumption.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/W523793/1 30/09/2021 29/09/2025
2737745 Studentship EP/W523793/1 02/10/2022 29/09/2026 Marc Truter