Notes on the Hodge conjecture for Fermat varieties
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 a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2021-01-01
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| Series: | Experimental Results |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2516712X21000149/type/journal_article |
| _version_ | 1797851645520904192 |
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| author | Genival da Silva Adrian Clingher |
| author_facet | Genival da Silva Adrian Clingher |
| author_sort | Genival da Silva |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T19:21:07Z |
| format | Article |
| id | doaj.art-59a8d3bea8b445fa8a056d9b35bafa79 |
| institution | Directory Open Access Journal |
| issn | 2516-712X |
| language | English |
| last_indexed | 2024-04-09T19:21:07Z |
| publishDate | 2021-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Experimental Results |
| spelling | doaj.art-59a8d3bea8b445fa8a056d9b35bafa792023-04-05T13:04:24ZengCambridge University PressExperimental Results2516-712X2021-01-01210.1017/exp.2021.14Notes on the Hodge conjecture for Fermat varietiesGenival da Silva0https://orcid.org/0000-0002-8667-8255Adrian Clingher1Department of Mathematics, Eastern Illinois University, Charleston, IL, USAUniversity of Missouri at Saint Louis, Mathematics and Computer Science, One University Blvd, St. Louis, Missouri, United States, 63121 UMSLWe 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.https://www.cambridge.org/core/product/identifier/S2516712X21000149/type/journal_article |
| spellingShingle | Genival da Silva Adrian Clingher Notes on the Hodge conjecture for Fermat varieties Experimental Results |
| title | Notes on the Hodge conjecture for Fermat varieties |
| title_full | Notes on the Hodge conjecture for Fermat varieties |
| title_fullStr | Notes on the Hodge conjecture for Fermat varieties |
| title_full_unstemmed | Notes on the Hodge conjecture for Fermat varieties |
| title_short | Notes on the Hodge conjecture for Fermat varieties |
| title_sort | notes on the hodge conjecture for fermat varieties |
| url | https://www.cambridge.org/core/product/identifier/S2516712X21000149/type/journal_article |
| work_keys_str_mv | AT genivaldasilva notesonthehodgeconjectureforfermatvarieties AT adrianclingher notesonthehodgeconjectureforfermatvarieties |