Messanae Universitas Studiorum: No conditions. Results ordered -Date Deposited. 2017-10-17T20:42:10ZEPrintshttp://cab.unime.it/images/sitelogo.pnghttp://cab.unime.it/mus/2012-09-19T07:53:02Z2013-06-19T09:10:23Zhttp://cab.unime.it/mus/id/eprint/629This item is in the repository with the URL: http://cab.unime.it/mus/id/eprint/6292012-09-19T07:53:02ZSulle sezioni di un fascio riflessivo di rango 2 su $P^3$:
casi estremi per la prima sezioneIf $F$ is a rank two normalized reflexive sheaf on $P^3$ with first chern class 0 or -1, it is possible to define the integers $ \alpha \ $ =smallest number such that $F(\alpha \ )$ has a non-vanishing section and $ \beta \ $ =smallest number such that $F( \beta \ )$ has a new sectiot, not multiple of one section of $F( \alpha \ )$. Then it is well known that the zero-locus of a non-vanishing general section of $F(t)$ gives rise to a locally Choen-Macaulay, almost everywhere complete intersection curve if and only if either $t= \alpha \ or \t \ge \ \beta \ $. Moreover in $[H_2]$ it is proved that $\alpha\le\sqrt{3c_2+1+3c_1 / 4}-1-{c_1 / 2}$ (the $c_i$'s being the chern classes of $F$).
In this paper it is shown that, ig $ \alpha\ $ is as high as possible, i.e. $ \alpha\ $ =integral part of $\alpha\le\sqrt{3c_2+1+3c_1 / 4}-1-{c_1 / 2}$ , then alpha=beta and moreover $h^2$ F(alpha)=0Margherita RoggeroPaolo Valabrega2009-11-25Z2010-04-13T11:15:21Zhttp://cab.unime.it/mus/id/eprint/519This item is in the repository with the URL: http://cab.unime.it/mus/id/eprint/5192009-11-25ZA few splitting theorems for rank 2 vector bundles on P4
The paper investigates vanishing conditions on the intermediate cohomology of a normalized rank 2 vector bundle on which force to split or, at least, to be a non-stable bundle (with few possible exceptions). The results are applied to see when subcanonical surfaces in are forced to be complete intersections of two hypersurfaces, since subcanonical surfaces are zero loci of non-zero sections of rank vector bundles.
Margherita RoggeroPaolo Valabrega