On a conjecture of harris
For d ≥ 4, the Noether-Lefschetz locus NLd parametrizes smooth, degree d sur- faces in P3 with Picard number at least 2. A conjecture of Harris states that there are only finitely many irreducible components of the Noether-Lefschetz locus of non-maximal codimen- sion. Voisin showed that the conjectu...
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1175 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1175 https://doi.org/10.1142/S0219199720500285 |
| Access Level: | acceso abierto |
| Palabra clave: | Harris conjecture Noether-Lefschetz locus Hodge locus flag Hilbert schemes |
| Sumario: | For d ≥ 4, the Noether-Lefschetz locus NLd parametrizes smooth, degree d sur- faces in P3 with Picard number at least 2. A conjecture of Harris states that there are only finitely many irreducible components of the Noether-Lefschetz locus of non-maximal codimen- sion. Voisin showed that the conjecture is false for sufficiently large d, but is true for d ≤ 5. She also showed that for d = 6, 7, there are finitely many reduced, irreducible components of NLd of non-maximal codimension. In this article, we prove that for any d ≥ 6, there are infinitely many non-reduced irreducible components of NLd of non-maximal codimension. |
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