Preprint C1445/2019
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.