On the jumping lines of bundles of logarithmic vector fields along plane curves
Dimca, Alexandru (Université Côte d'Azur)
Sticlaru, Gabriel (Ovidius University (Constanta, Romania). Faculty of Mathematics and Informatics)

Date:	2020
Abstract:	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.
Note:	This work has been partially supported by the French government, through the UCAJEDI Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-15-IDEX-01 and by the Romanian Ministry of Research and Innovation, CNCS - UEFISCDI, grant PN-III-P4-ID-PCE2016-0030, within PNCDI III.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Plane curve ; Vector bundle ; Stable bundle ; Splitting type ; Jumping line ; Jacobian module ; Logarithmic vector fields
Published in:	Publicacions matemàtiques, Vol. 64 Núm. 2 (2020) , p. 513-542 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/371196
DOI: 10.5565/PUBLMAT6422006

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