Lefschetz properties, Laplace equations and Galois coverings

Abstract: In an article in collaboration with Rosa M. Mirò-Roig and Giorgio Ottaviani (Canad. J. Math. 65, 2013), we established a relation, due to apolarity, between Artinian homogeneous ideals of a polynomial ring not satisfying the Weak Lefschetz Property - WLP - and projective varieties that verify a Laplace equation of a certain order s, i.e. such that all the s-osculating spaces have dimension less than expected. Thanks to this relation, it is possible to extend to various classes of toric varieties some classical results due to Eugenio Togliatti. In the seminar, I will introduce these notions and I will speak of some recent results in collaboration with Liena Colarte and Rosa M. Miro'-Roig, relating them to cyclic Galois coverings.

MathematicsPhysics

Audience: researchers in the discipline

Seminario de Geometría y Física - Matemática UCN-USP