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Zbl 1139.14019
Vallès, Jean
Logarithmic vector bundles on the projective plan. (Fibrés logarithmiques sur le plan projectif.) (French. English summary)
[J] Ann. Fac. Sci. Toulouse, Math. (6) 16, No. 2, 385-395 (2007). ISSN 0240-2963

The author describes the scheme of jumping lines of a logarithmic bundle on the projective plane, with odd first Chern class. In this way he completes a result already known for logarithmic bundles of the projective plane with even first Chern class [{\it I. Dolgachev, M. Kapranov}, Duke Math. J. 71, 633--664, (1993; Zbl 0804.14007)]. For the `odd' case, he obtains a description of this scheme adding a finite set of lines to the ones of the divisor of the bundle; this set of lines comes from a connection between the logarithmic bundle and the associated ideal sheaf of the group of points in the projective dual space. The author also gives some explicit constructions which enlighten the geometric meaning of the main result of the paper.
[Cristina Bertone (Torino)]

MSC 2000:: *14F05 Sheaves, etc.
14J60 Vector bundles on surfaces and higher-order varieties

Keywords: logarithmic bundle; jumping line

Citations: Zbl 0804.14007

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