Bad loci of free linear systems
| dc.creator | de Fernex, Tommaso | |
| dc.creator | Lanteri, Antonio | |
| dc.date | 2004-09-26 | |
| dc.date.accessioned | 2026-07-07T05:12:35Z | |
| dc.date.available | 2026-07-07T05:12:35Z | |
| dc.description | The bad locus of a base-point free linear system L on a normal complex projective variety X is defined as the subset B(L) of X of points that are not contained in any irreducible and reduced member of L. In this paper we provide a geometric description of such locus in terms of the morphism defined by L. In particular, assume that the dimension of X is at least 2, and that L is the complete linear system associated to an ample and spanned line bundle. It is known that in this case B(L) is empty unless X is a surface. Then we prove that, when the latter occurs, B(L) is not empty if and only if L defines a morphism onto a two dimensional cone, in which case B(L) is the inverse image of the vertex of the cone. | |
| dc.description | 13 pages; to appear in Adv. Geom | |
| dc.identifier | https://arxiv.org/abs/math/0409499 | |
| dc.identifier | http://arxiv.org/abs/math/0409499 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72628 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C20 (primary); 14J25 (secondary) | |
| dc.title | Bad loci of free linear systems | |
| dc.type | text |