SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES
In this paper we study the singularities of the invariant metric of the Poincaré bundle over a family of abelian varieties and their duals over a base of arbitrary dimension. As an application of this study we prove the effectiveness of the height jump divisors for families of pointed abelian variet...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2018-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509418000130/type/journal_article |
| _version_ | 1811156227188588544 |
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| author | JOSÉ IGNACIO BURGOS GIL DAVID HOLMES ROBIN DE JONG |
| author_facet | JOSÉ IGNACIO BURGOS GIL DAVID HOLMES ROBIN DE JONG |
| author_sort | JOSÉ IGNACIO BURGOS GIL |
| collection | DOAJ |
| description | In this paper we study the singularities of the invariant metric of the Poincaré bundle over a family of abelian varieties and their duals over a base of arbitrary dimension. As an application of this study we prove the effectiveness of the height jump divisors for families of pointed abelian varieties. The effectiveness of the height jump divisor was conjectured by Hain in the more general case of variations of polarized Hodge structures of weight
$-1$
. |
| first_indexed | 2024-04-10T04:47:01Z |
| format | Article |
| id | doaj.art-40876d20b5c946b28e26b540b38623ba |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:01Z |
| publishDate | 2018-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-40876d20b5c946b28e26b540b38623ba2023-03-09T12:34:35ZengCambridge University PressForum of Mathematics, Sigma2050-50942018-01-01610.1017/fms.2018.13SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIESJOSÉ IGNACIO BURGOS GIL0DAVID HOLMES1ROBIN DE JONG2Instituto de Ciencias Matemáticas (CSIC-UAM-UCM-UCM3), Calle Nicolás Cabrera 15, Campus UAM, Cantoblanco, 28049 Madrid, Spain;Mathematical Institute, Leiden University, PO Box 9512, 2300 RA Leiden, The Netherlands; ,Mathematical Institute, Leiden University, PO Box 9512, 2300 RA Leiden, The Netherlands; ,In this paper we study the singularities of the invariant metric of the Poincaré bundle over a family of abelian varieties and their duals over a base of arbitrary dimension. As an application of this study we prove the effectiveness of the height jump divisors for families of pointed abelian varieties. The effectiveness of the height jump divisor was conjectured by Hain in the more general case of variations of polarized Hodge structures of weight $-1$ .https://www.cambridge.org/core/product/identifier/S2050509418000130/type/journal_article14H10 (primary)11G5014D07 (secondary) |
| spellingShingle | JOSÉ IGNACIO BURGOS GIL DAVID HOLMES ROBIN DE JONG SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES Forum of Mathematics, Sigma 14H10 (primary) 11G50 14D07 (secondary) |
| title | SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES |
| title_full | SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES |
| title_fullStr | SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES |
| title_full_unstemmed | SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES |
| title_short | SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES |
| title_sort | singularities of the biextension metric for families of abelian varieties |
| topic | 14H10 (primary) 11G50 14D07 (secondary) |
| url | https://www.cambridge.org/core/product/identifier/S2050509418000130/type/journal_article |
| work_keys_str_mv | AT joseignacioburgosgil singularitiesofthebiextensionmetricforfamiliesofabelianvarieties AT davidholmes singularitiesofthebiextensionmetricforfamiliesofabelianvarieties AT robindejong singularitiesofthebiextensionmetricforfamiliesofabelianvarieties |