A conjecture of Beauville and Catanese revisited
A theorem of Green, Lazarsfeld and Simpson (formerly a conjecture of Beauville and Catanese) states that certain naturally defined subvarieties of the Picard variety of a smooth projective complex variety are unions of translates of abelian subvarieties by torsion points. Their proof uses analytic m...
| Hauptverfasser: | , |
|---|---|
| Format: | Journal article |
| Veröffentlicht: |
Springer
2004
|
| _version_ | 1826256719171289088 |
|---|---|
| author | Pink, R Roessler, D |
| author_facet | Pink, R Roessler, D |
| author_sort | Pink, R |
| collection | OXFORD |
| description | A theorem of Green, Lazarsfeld and Simpson (formerly a conjecture of Beauville and Catanese) states that certain naturally defined subvarieties of the Picard variety of a smooth projective complex variety are unions of translates of abelian subvarieties by torsion points. Their proof uses analytic methods. We refine and give a completely new proof of their result. Our proof combines galois-theoretic methods and algebraic geometry in positive characteristic. When the variety has a model over a function field and its Picard variety has no isotrivial factors, we show how to replace the galois-theoretic results we need by results from model theory (mathematical logic). Furthermore, we prove partial analogs of the conjecture of Beauville and Catanese in positive characteristic. |
| first_indexed | 2024-03-06T18:06:43Z |
| format | Journal article |
| id | oxford-uuid:01ace23e-03f5-4e8e-a55a-7220f7c2e237 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:06:43Z |
| publishDate | 2004 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:01ace23e-03f5-4e8e-a55a-7220f7c2e2372022-03-26T08:36:20ZA conjecture of Beauville and Catanese revisitedJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:01ace23e-03f5-4e8e-a55a-7220f7c2e237Symplectic Elements at OxfordSpringer2004Pink, RRoessler, DA theorem of Green, Lazarsfeld and Simpson (formerly a conjecture of Beauville and Catanese) states that certain naturally defined subvarieties of the Picard variety of a smooth projective complex variety are unions of translates of abelian subvarieties by torsion points. Their proof uses analytic methods. We refine and give a completely new proof of their result. Our proof combines galois-theoretic methods and algebraic geometry in positive characteristic. When the variety has a model over a function field and its Picard variety has no isotrivial factors, we show how to replace the galois-theoretic results we need by results from model theory (mathematical logic). Furthermore, we prove partial analogs of the conjecture of Beauville and Catanese in positive characteristic. |
| spellingShingle | Pink, R Roessler, D A conjecture of Beauville and Catanese revisited |
| title | A conjecture of Beauville and Catanese revisited |
| title_full | A conjecture of Beauville and Catanese revisited |
| title_fullStr | A conjecture of Beauville and Catanese revisited |
| title_full_unstemmed | A conjecture of Beauville and Catanese revisited |
| title_short | A conjecture of Beauville and Catanese revisited |
| title_sort | conjecture of beauville and catanese revisited |
| work_keys_str_mv | AT pinkr aconjectureofbeauvilleandcataneserevisited AT roesslerd aconjectureofbeauvilleandcataneserevisited AT pinkr conjectureofbeauvilleandcataneserevisited AT roesslerd conjectureofbeauvilleandcataneserevisited |