Notes on the Hodge conjecture for Fermat varieties. (16th July 2021)

• Record Type: Journal Article
• Authors: Clingher, Adrian; da Silva, Genival
• Is Part Of: Experimental results. Volume 2(2021)
• Publication Date: 2021-07-16
• Subjects: Science -- Experiments -- Periodicals; Science -- Methodology -- Periodicals; 507.24
• DOI: 10.1017/exp.2021.14
• Languages: English
• ISSNs: 2516-712X

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.