Periods of Algebraic Cycles

Roberto Tomás Villaflor Loyola

**Keywords:**Periods | algebraic cycles | variational Hodge conjecture

We compute periods of algebraic cycles inside smooth even dimensional hypersurfaces of the

complex projective space. We consider the explicit description in Cech cohomology (due to

Carlson and Griffiths) of the basis for the primitive De Rham cohomology of the given

hypersurface. And use it to compute periods of algebraic cycles supported in algebraic

subvarieties of the hypersurface which are complete intersections in the ambient projective

space. As an application, we use the explicit description of the Infinitesimal Variations of

Hodge Structures in terms of periods, to prove variational Hodge conjecture for certain

combinations of linear cycles inside Fermat varieties.