Abstract
Abstract
We review a combinatoric approach to the Hodge conjecture for Fermat varieties and announce new cases where the conjecture is true. We show the Hodge conjecture for Fermat fourfolds
$ {X}_m^4 $
of degree m ≤ 100 coprime to 6, and also prove the conjecture for
$ {X}_{21}^n $
and
$ {X}_{27}^n $
, for all n.
Publisher
Cambridge University Press (CUP)
Reference7 articles.
1. The Hodge conjecture and arithmetic quotients of complex balls
2. The hodge conjecture for Fermat varieties
3. Markman, E. (2021). The monodromy of generalized Kummer varieties and algebraic cycles on their intermediate Jacobians. Preprint, arXiv:1805.11574.
4. Some new algebraic cycles on Fermat varieties