Gushel--Mukai varieties: intermediate Jacobians
We describe intermediate Jacobians of Gushel-Mukai varieties $X$ of dimensions 3 or 5: if $A$ is the Lagrangian space associated with $X$, we prove that the intermediate Jacobian of $X$ is isomorphic to the Albanese variety of the canonical double covering of any of the two dual Eisenbud-Popescu-Wal...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Association Epiga
2020-12-01
|
| Series: | Épijournal de Géométrie Algébrique |
| Subjects: | |
| Online Access: | https://epiga.episciences.org/6475/pdf |
| _version_ | 1798029634091089920 |
|---|---|
| author | Olivier Debarre Alexander Kuznetsov |
| author_facet | Olivier Debarre Alexander Kuznetsov |
| author_sort | Olivier Debarre |
| collection | DOAJ |
| description | We describe intermediate Jacobians of Gushel-Mukai varieties $X$ of
dimensions 3 or 5: if $A$ is the Lagrangian space associated with $X$, we prove
that the intermediate Jacobian of $X$ is isomorphic to the Albanese variety of
the canonical double covering of any of the two dual Eisenbud-Popescu-Walter
surfaces associated with $A$. As an application, we describe the period maps
for Gushel-Mukai threefolds and fivefolds. |
| first_indexed | 2024-04-11T19:28:25Z |
| format | Article |
| id | doaj.art-46c251159c7b42daa138b34d30fefc59 |
| institution | Directory Open Access Journal |
| issn | 2491-6765 |
| language | English |
| last_indexed | 2024-04-11T19:28:25Z |
| publishDate | 2020-12-01 |
| publisher | Association Epiga |
| record_format | Article |
| series | Épijournal de Géométrie Algébrique |
| spelling | doaj.art-46c251159c7b42daa138b34d30fefc592022-12-22T04:07:04ZengAssociation EpigaÉpijournal de Géométrie Algébrique2491-67652020-12-01Volume 410.46298/epiga.2020.volume4.64756475Gushel--Mukai varieties: intermediate JacobiansOlivier DebarreAlexander KuznetsovWe describe intermediate Jacobians of Gushel-Mukai varieties $X$ of dimensions 3 or 5: if $A$ is the Lagrangian space associated with $X$, we prove that the intermediate Jacobian of $X$ is isomorphic to the Albanese variety of the canonical double covering of any of the two dual Eisenbud-Popescu-Walter surfaces associated with $A$. As an application, we describe the period maps for Gushel-Mukai threefolds and fivefolds.https://epiga.episciences.org/6475/pdfmathematics - algebraic geometry14j45, 14j35, 14j40, 14m15 |
| spellingShingle | Olivier Debarre Alexander Kuznetsov Gushel--Mukai varieties: intermediate Jacobians Épijournal de Géométrie Algébrique mathematics - algebraic geometry 14j45, 14j35, 14j40, 14m15 |
| title | Gushel--Mukai varieties: intermediate Jacobians |
| title_full | Gushel--Mukai varieties: intermediate Jacobians |
| title_fullStr | Gushel--Mukai varieties: intermediate Jacobians |
| title_full_unstemmed | Gushel--Mukai varieties: intermediate Jacobians |
| title_short | Gushel--Mukai varieties: intermediate Jacobians |
| title_sort | gushel mukai varieties intermediate jacobians |
| topic | mathematics - algebraic geometry 14j45, 14j35, 14j40, 14m15 |
| url | https://epiga.episciences.org/6475/pdf |
| work_keys_str_mv | AT olivierdebarre gushelmukaivarietiesintermediatejacobians AT alexanderkuznetsov gushelmukaivarietiesintermediatejacobians |