29 apr 2022 -- 17:00
Geometry in Como (online)
Abstract.
Jacobian rings are a powerful tool for the study of the geometric properties of hypersurfaces in projective spaces. These rings have a rich algebraic structure as they are examples of peculiar Artinian algebras. A long standing problem for this kind of algebras is whether, under specific assumptions, Lefschetz properties hold or do not hold. Unfortunately, the known results are a few, when compared to what has yet to be analysed; moreover, also restricting to the case of jacobian rings, these properties have been shown only for small dimensions and small degrees. In this seminar, we will present geometric-differential techniques that allow us to prove some Lefschetz properties for some of the first open cases: the jacobian rings of cubic fourfolds (and threefolds). This seminary is based on a preprint in collaboration with Gian Pietro Pirola (arXiv:2201.07550) and on a work in progress.