Speaker: Jorge Duque.
Date: 10:30 11/03/2022
Title: On fake linear cycles inside Fermat varieties.

Abstract: We introduce a new class of Hodge cycles with non-reduced associated Hodge loci, we call them fake linear cycles. We characterize them for all Fermat varieties and show that they exist only for degrees $d=3,4,6$, where there are infinitely many in the space of Hodge cycles. These cycles are pathological in the sense that the Zariski tangent space of their associated Hodge locus is of maximal dimension, contrary to a conjecture of Movasati. Moreover they provide examples of algebraic cycles not generated by their periods in the sense of Movasati-Sert\"oz. This is joint work with Roberto Villaflor.