On the jumping lines of bundles of logarithmic vector fields along plane curves
For a reduced curve C : f = 0 in the complex projective plane P 2 , we study the set of jumping lines for the rank two vector bundle ThCi on P 2 whose sections are the logarithmic vector fields along C. We point out the relations of these jumping lines with the Lefschetz type properties of the Jacob...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:225701 |
| Acceso en línea: | https://ddd.uab.cat/record/225701 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6422006 |
| Access Level: | acceso abierto |
| Palabra clave: | Plane curve Vector bundle Stable bundle Splitting type Jumping line Jacobian module Logarithmic vector fields |
| Sumario: | For a reduced curve C : f = 0 in the complex projective plane P 2 , we study the set of jumping lines for the rank two vector bundle ThCi on P 2 whose sections are the logarithmic vector fields along C. We point out the relations of these jumping lines with the Lefschetz type properties of the Jacobian module of f and with the Bourbaki ideal of the module of Jacobian syzygies of f. In particular, when the vector bundle ThCi is unstable, a line is a jumping line if and only if it meets the 0-dimensional subscheme defined by this Bourbaki ideal, a result going back to Schwarzenberger. Other classical general results by Barth, Hartshorne, and Hulek resurface in the study of this special class of rank two vector bundles. |
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