Seminario - Developable cubics in P^4 and the Lefschetz locus in GOR(1,5,5,1)
Il giorno 9 Ottobre alle ore 15,30 in Aula Anile il Prof. Rodrigo Gondim Neves (Università Federal Rural de Pernambuco di Recife-Brasile) terrà un seminario dal titolo:
Developable cubics in P^4 and the Lefschetz locus in GOR(1,5,5,1)
(Joint with T. Fassarela and V. Ferrer)
Abstract: We classify, up to projective transformations, the developable cubic
hypersurfaces in P^4 that are not cones. They correspond to hyperplane
sections of the secant variety of the Veronese surface V(2,2) \in P^5.
There are three distinct classes. From Macaulay-Matlis duality we
investigate the associated algebras in GOR(1,5,5,1), the space of
standard graded Artinian Gorenstein algebras whose Hilbert vector is
(1,5,5,1). The viewpoint of was to find their Jordan types and
describe the classes that have the Strong Lefschetz properties. Two of
these classes have the SLP. We describe the locus GOR(1,5,5,1) from
this perspective and we determine the locus X \subset GOR(1,5,5,1) of
algebras that do not satisfy the Lefschetz property. While the algebras with the SLP have Jordan type (4,2,2,2,2), the algebras of X have Jordan type (4, 2, 2, 2, 1, 1).