Notes on the Hodge conjecture for Fermat varieties. (16th July 2021) - Clingher, Adrian; da Silva, Genival
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.