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Hodge numbers from Picard-Fuchs equations
Given a variation of Hodge structure over P 1 with Hodge numbers (1, 1, . . . , 1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin–Kontsevich–M¨oller–Zorich, by using the local exponents of the corresponding Picard–Fuchs equation. This allows us to...
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| Format: | Default Article |
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2017
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| Online Access: | https://hdl.handle.net/2134/34898 |
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| _version_ | 1818169343801819136 |
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| author | Charles F. Doran Andrew Harder Alan Thompson |
| author_facet | Charles F. Doran Andrew Harder Alan Thompson |
| author_sort | Charles F. Doran (7160870) |
| collection | Figshare |
| description | Given a variation of Hodge structure over P 1 with Hodge numbers (1, 1, . . . , 1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin–Kontsevich–M¨oller–Zorich, by using the local exponents of the corresponding Picard–Fuchs equation. This allows us to compute the Hodge numbers of Zucker’s Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi–Yau threefolds. |
| format | Default Article |
| id | rr-article-9387140 |
| institution | Loughborough University |
| publishDate | 2017 |
| record_format | Figshare |
| spelling | rr-article-93871402017-06-18T00:00:00Z Hodge numbers from Picard-Fuchs equations Charles F. Doran (7160870) Andrew Harder (7065845) Alan Thompson (5686433) Other mathematical sciences not elsewhere classified Variation of Hodge structures Calabi–Yau manifolds Mathematical Sciences not elsewhere classified Given a variation of Hodge structure over P 1 with Hodge numbers (1, 1, . . . , 1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin–Kontsevich–M¨oller–Zorich, by using the local exponents of the corresponding Picard–Fuchs equation. This allows us to compute the Hodge numbers of Zucker’s Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi–Yau threefolds. 2017-06-18T00:00:00Z Text Journal contribution 2134/34898 https://figshare.com/articles/journal_contribution/Hodge_numbers_from_Picard-Fuchs_equations/9387140 CC BY-SA 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified Variation of Hodge structures Calabi–Yau manifolds Mathematical Sciences not elsewhere classified Charles F. Doran Andrew Harder Alan Thompson Hodge numbers from Picard-Fuchs equations |
| title | Hodge numbers from Picard-Fuchs equations |
| title_full | Hodge numbers from Picard-Fuchs equations |
| title_fullStr | Hodge numbers from Picard-Fuchs equations |
| title_full_unstemmed | Hodge numbers from Picard-Fuchs equations |
| title_short | Hodge numbers from Picard-Fuchs equations |
| title_sort | hodge numbers from picard-fuchs equations |
| topic | Other mathematical sciences not elsewhere classified Variation of Hodge structures Calabi–Yau manifolds Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/34898 |