Why should one compute periods of algebraic cycles?

Research paper by Hossein Movasati

Indexed on: 21 Feb '16Published on: 21 Feb '16Published in: Mathematics - Algebraic Geometry


In this article we show how the data of integrals of algebraic differential forms over algebraic cycles can be used in order to prove that algebraic and Hodge cycle deformations of a given algebraic cycle are equivalent. We verify this equivalence for linear projective spaces inside hypersurfaces. We also prove that most of the Hodge and algebraic cycles of the Fermat sextic fourfold cannot be deformed in the moduli space of sextic fourfold hypersurfaces.