Periods of elliptic surfaces with $p_g=q=1$
We prove that the period mapping is dominant for elliptic surfaces over an elliptic curve with $12$ nodal fibers, and that its degree is larger than $1$ . This settles the final case of infinitesimal Torelli for a generic elliptic surface.
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2024-01-01
|
| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424000859/type/journal_article |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850067038010081280 |
|---|---|
| author | Philip Engel François Greer Abigail Ward |
| author_facet | Philip Engel François Greer Abigail Ward |
| author_sort | Philip Engel |
| collection | DOAJ |
| description | We prove that the period mapping is dominant for elliptic surfaces over an elliptic curve with
$12$
nodal fibers, and that its degree is larger than
$1$
. This settles the final case of infinitesimal Torelli for a generic elliptic surface. |
| format | Article |
| id | doaj-art-4be5dce5cc3d4b83ba0623071962d4cc |
| institution | DOAJ |
| issn | 2050-5094 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-4be5dce5cc3d4b83ba0623071962d4cc2025-08-20T02:48:30ZengCambridge University PressForum of Mathematics, Sigma2050-50942024-01-011210.1017/fms.2024.85Periods of elliptic surfaces with $p_g=q=1$Philip Engel0https://orcid.org/0000-0003-4900-9383François Greer1https://orcid.org/0000-0002-9350-435XAbigail Ward2Mathematisches Institut, University of Bonn, Bonn 53115, Germany; E-mail:Department of Mathematics, Michigan State University, East Lansing MI 48824, USACentre for Mathematical Sciences, Cambridge University, Cambridge CB3 0WA, UK; E-mail:We prove that the period mapping is dominant for elliptic surfaces over an elliptic curve with $12$ nodal fibers, and that its degree is larger than $1$ . This settles the final case of infinitesimal Torelli for a generic elliptic surface.https://www.cambridge.org/core/product/identifier/S2050509424000859/type/journal_article14J2714D07 |
| spellingShingle | Philip Engel François Greer Abigail Ward Periods of elliptic surfaces with $p_g=q=1$ Forum of Mathematics, Sigma 14J27 14D07 |
| title | Periods of elliptic surfaces with $p_g=q=1$ |
| title_full | Periods of elliptic surfaces with $p_g=q=1$ |
| title_fullStr | Periods of elliptic surfaces with $p_g=q=1$ |
| title_full_unstemmed | Periods of elliptic surfaces with $p_g=q=1$ |
| title_short | Periods of elliptic surfaces with $p_g=q=1$ |
| title_sort | periods of elliptic surfaces with p g q 1 |
| topic | 14J27 14D07 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424000859/type/journal_article |
| work_keys_str_mv | AT philipengel periodsofellipticsurfaceswithpgq1 AT francoisgreer periodsofellipticsurfaceswithpgq1 AT abigailward periodsofellipticsurfaceswithpgq1 |