2020
DOI: 10.5565/publmat6422006
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On the jumping lines of bundles of logarithmic vector fields along plane curves

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 T C 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 T C is unstable, a line is a jumping line if and only if it meets the 0-dimensional subschem… Show more

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Cited by 4 publications
(3 citation statements)
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“…This fact implies that C 2 is a jumping line for E C 1 in the case (1). The claim in case (2) follows from [12,Corollary 4.6 and Example 4.8]. Indeed, these results imply that we have…”
Section: And Hence the Condition 2rmentioning
confidence: 72%
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“…This fact implies that C 2 is a jumping line for E C 1 in the case (1). The claim in case (2) follows from [12,Corollary 4.6 and Example 4.8]. Indeed, these results imply that we have…”
Section: And Hence the Condition 2rmentioning
confidence: 72%
“…Using for instance [12,Example 4.8] we see that in this case d L 0 1 (C 1 ) = r 1 . The same equality holds for all the other non free reduced plane curves C 1 satisfying 2r 1 < d 1 , see [12,Corollary 4.5]. This fact implies that C 2 is a jumping line for E C 1 in the case (1).…”
Section: And Hence the Condition 2rmentioning
confidence: 99%
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