Let U be a very ample vector bundle of rank 2 on P^2 with c_1=4, c_2=6. The associated scroll (X,H), a Bordiga scroll of degree 10, turns out to be isomorphic to the blowing-up of P^3 along a twisted cubic C. Then the jumping lines and conics of U can be described in a very easy and explicit way through the geometry of C.
Remarks on the Bordiga scrolls of degree ten / A. Lanteri, V. Nannola. - In: JP JOURNAL OF ALGEBRA, NUMBER THEORY AND APPLICATIONS. - ISSN 0972-5555. - 13:2(2009), pp. 209-219.
Remarks on the Bordiga scrolls of degree ten
A. LanteriPrimo
;
2009
Abstract
Let U be a very ample vector bundle of rank 2 on P^2 with c_1=4, c_2=6. The associated scroll (X,H), a Bordiga scroll of degree 10, turns out to be isomorphic to the blowing-up of P^3 along a twisted cubic C. Then the jumping lines and conics of U can be described in a very easy and explicit way through the geometry of C.
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