Integral Hodge conjecture for Fermat varieties
Algebraic Geometry
2019-05-24 v2 Algebraic Topology
Number Theory
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.
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Cite
@article{arxiv.1711.02628,
title = {Integral Hodge conjecture for Fermat varieties},
author = {Enzo Aljovin and Hossein Movasati and Roberto Villaflor Loyola},
journal= {arXiv preprint arXiv:1711.02628},
year = {2019}
}
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7 pages