The connectedness of degeneracy loci in positive characteristic
A well-known result of Fulton–Lazarsfeld ensures the connectedness of degeneracy loci under an ampleness condition. We extend it to positive characteristic, along with the variants for degeneracy loci of symmetric and alternating maps of even rank, due to Tu in characteristic zero. The proof uses th...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.448/ |
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| author | Lodh, Rémi |
| author_facet | Lodh, Rémi |
| author_sort | Lodh, Rémi |
| collection | DOAJ |
| description | A well-known result of Fulton–Lazarsfeld ensures the connectedness of degeneracy loci under an ampleness condition. We extend it to positive characteristic, along with the variants for degeneracy loci of symmetric and alternating maps of even rank, due to Tu in characteristic zero. The proof uses the explicit determination of the top étale cohomology group of an algebraic variety, a result communicated by Esnault. |
| format | Article |
| id | doaj-art-5701c7b2d3fe45c29a5e887e23dba683 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-5701c7b2d3fe45c29a5e887e23dba6832025-02-07T11:09:17ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-09-01361G695996410.5802/crmath.44810.5802/crmath.448The connectedness of degeneracy loci in positive characteristicLodh, Rémi0Springer-Verlag, Tiergartenstr. 17, 69121 Heidelberg, GermanyA well-known result of Fulton–Lazarsfeld ensures the connectedness of degeneracy loci under an ampleness condition. We extend it to positive characteristic, along with the variants for degeneracy loci of symmetric and alternating maps of even rank, due to Tu in characteristic zero. The proof uses the explicit determination of the top étale cohomology group of an algebraic variety, a result communicated by Esnault.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.448/ |
| spellingShingle | Lodh, Rémi The connectedness of degeneracy loci in positive characteristic Comptes Rendus. Mathématique |
| title | The connectedness of degeneracy loci in positive characteristic |
| title_full | The connectedness of degeneracy loci in positive characteristic |
| title_fullStr | The connectedness of degeneracy loci in positive characteristic |
| title_full_unstemmed | The connectedness of degeneracy loci in positive characteristic |
| title_short | The connectedness of degeneracy loci in positive characteristic |
| title_sort | connectedness of degeneracy loci in positive characteristic |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.448/ |
| work_keys_str_mv | AT lodhremi theconnectednessofdegeneracylociinpositivecharacteristic AT lodhremi connectednessofdegeneracylociinpositivecharacteristic |