On the jumping conics of a semistable rank two vector bundle on P2 |
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Authors: | Mirella Manaresi |
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Affiliation: | (1) Dipartimento di Matematica-Università, P. za di Porta S. Donato, 5, I-40127 Bologna, (Italy) |
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Abstract: | Stromme (see [S], (1.7)) introduced the notion of jumping conic of a normalized semistable rank two vector bundle E on ℙ2 and he remarked that the locus of jumping conics of E has codimension ≤3+2c1(E), with equality for general E. Here we introduce a concept of jumping conic of a semistable rank two vector bundle on ℙ2 (see (I.1)) by generalizing the notion of jumping line of the second kind introduced by Hulek in [H]. Our definition agrees with Stromme's for c1=−1, but not for c1=0. In contrast with the case of jumping lines, where we have a different behaviour in the case c1 even or c1 odd, the set of jumping conics according to our definition is always a divisor (possibly empty) in the ℙ5 of all conics of ℙ2 (see th. (I.8)), whose degree depends on c2(E). |
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