Hodge theory on cyclotomic threefolds (with a view towards the higher dimensional case)
Translation of the Italian summary: In the present work, one considers a family of smooth hypersurfaces of the four-dimensional complex projective space, which are invariant under the action of the group of \(p\)-th roots of unity where \(p\) is a divisor of the degree. One verifies the Grothendieck-Hodge conjecture about the general element of the considered family by generalizing a method of G. E. Walters, or alternatively by exhibiting a relation between the Miyaoka-Mori uniruledness conjecture and the mentioned Hodge conjecture on first filtration of the intermediate cohomology. The same construction can be applied to the analogue family of hypersurfaces of the \((n+1)\)-dimensional complex projective space obtaining similar results. In particular, one exhibits a countable number of families of fourfolds which verify the classical \((2,2)\)-Hodge conjecture.
scientific article; zbMATH DE number 1471600
scientific article