Hodge theory on cyclotomic threefolds (with a view towards the higher dimensional case)
type: Item
instance of: scholarly article
title: Hodge theory on cyclotomic threefolds (with a view towards the higher dimensional case)
zbMATH Open document ID: 0974.14008
DOI: 10.1007/BF01783681
author: Michele Rossi
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2000-11-13T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 1471600
zbMATH Keywords: Hodge theory
zbMATH Keywords: cyclotomic threefolds
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1471600