Hodge Representations
Green–Griffiths–Kerr introduced Hodge representations to classify the Hodge groups of polarized Hodge structures, and the corresponding Mumford–Tate subdomains. We summarize how, given a fixed period domain $ \mathcal{D} $ , to enumerate the Hodge representations and corresponding Mumford–Tate su...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2020-01-01
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| Series: | Experimental Results |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2516712X20000556/type/journal_article |
| _version_ | 1797851683245522944 |
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| author | Xiayimei Han Colleen Robles Adrian Clingher |
| author_facet | Xiayimei Han Colleen Robles Adrian Clingher |
| author_sort | Xiayimei Han |
| collection | DOAJ |
| description | Green–Griffiths–Kerr introduced Hodge representations to classify the Hodge groups of polarized Hodge structures, and the corresponding Mumford–Tate subdomains. We summarize how, given a fixed period domain
$ \mathcal{D} $
, to enumerate the Hodge representations and corresponding Mumford–Tate subdomains
$ D \subset \mathcal{D} $
. The procedure is illustrated in two examples: (i) weight two Hodge structures with
$ {p}_g={h}^{2,0}=2 $
; and (ii) weight three CY-type Hodge structures. |
| first_indexed | 2024-04-09T19:21:49Z |
| format | Article |
| id | doaj.art-f3fb7c88200847898372a7d7fd790d7f |
| institution | Directory Open Access Journal |
| issn | 2516-712X |
| language | English |
| last_indexed | 2024-04-09T19:21:49Z |
| publishDate | 2020-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Experimental Results |
| spelling | doaj.art-f3fb7c88200847898372a7d7fd790d7f2023-04-05T13:04:14ZengCambridge University PressExperimental Results2516-712X2020-01-01110.1017/exp.2020.55Hodge RepresentationsXiayimei Han0Colleen Robles1https://orcid.org/0000-0002-5908-9551Adrian Clingher2Mathematics Department, Duke University, Box 90320, Durham, NC 27708-0320, USAMathematics Department, Duke University, Box 90320, Durham, NC 27708-0320, USAUniversity of Missouri at Saint Louis, Mathematics and Computer Science, One University Blvd, St. Louis, Missouri, United States, 63121 UMSLGreen–Griffiths–Kerr introduced Hodge representations to classify the Hodge groups of polarized Hodge structures, and the corresponding Mumford–Tate subdomains. We summarize how, given a fixed period domain $ \mathcal{D} $ , to enumerate the Hodge representations and corresponding Mumford–Tate subdomains $ D \subset \mathcal{D} $ . The procedure is illustrated in two examples: (i) weight two Hodge structures with $ {p}_g={h}^{2,0}=2 $ ; and (ii) weight three CY-type Hodge structures.https://www.cambridge.org/core/product/identifier/S2516712X20000556/type/journal_article58A14Hodge theory |
| spellingShingle | Xiayimei Han Colleen Robles Adrian Clingher Hodge Representations Experimental Results 58A14 Hodge theory |
| title | Hodge Representations |
| title_full | Hodge Representations |
| title_fullStr | Hodge Representations |
| title_full_unstemmed | Hodge Representations |
| title_short | Hodge Representations |
| title_sort | hodge representations |
| topic | 58A14 Hodge theory |
| url | https://www.cambridge.org/core/product/identifier/S2516712X20000556/type/journal_article |
| work_keys_str_mv | AT xiayimeihan hodgerepresentations AT colleenrobles hodgerepresentations AT adrianclingher hodgerepresentations |