Integral Hodge conjecture for Fermat varieties. (November 2019)

• Record Type: Journal Article
• Authors: Aljovin, Enzo; Movasati, Hossein; Villaflor Loyola, Roberto
• Is Part Of: Journal of symbolic computation. Volume 95(2019)
• Page Start: 177
• Page End: 184
• Publication Date: 2019-11
• Subjects: Hodge cycle -- Primitive cohomology -- Hodge filtration; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.02.006
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We describe an algorithm which verifies whether linear algebraic cycles of the Fermat variety generate the lattice of Hodge cycles. A computer implementation of this confirms the integral Hodge conjecture for quartic and quintic Fermat fourfolds. Our algorithm is based on computation of the list of elementary divisors of both the lattice of linear algebraic cycles, and the lattice of Hodge cycles written in terms of vanishing cycles, and observing that these two lists are the same.