Projective Q-factorial toric varieties covered by lines
| dc.creator | Casagrande, C. | |
| dc.creator | Di Rocco, S. | |
| dc.date | 2005-12-16 | |
| dc.date | 2007-01-19 | |
| dc.date.accessioned | 2026-07-07T07:41:41Z | |
| dc.date.available | 2026-07-07T07:41:41Z | |
| dc.description | The main result of this paper is a structural theorem for projective Q-factorial toric varieties X in P^N, covered by lines. We prove that there exists a toric fibration f: X -> Z, locally trivial in the Zariski topology, with fiber a product of projective joins. All lines in X intersecting the open subset isomorphic to the torus, are contained in some fiber of f. This characterization has a geometrical application to dual defective toric varieties, and a combinatorial application to discriminants of lattice subsets. We prove that X has positive dual defect if and only if it has an elementary extremal contraction of fiber type, whose general fiber is a projective join with dual defect bigger than its codimension in X. Turning to combinatorics, we characterize lattice subsets A with discriminant D_A equal to one, under suitable assumptions on the polytope Conv(A). | |
| dc.description | 24 pages. Refereed version, to appear in CCM (Communications in Contemporary Mathematics) | |
| dc.identifier | https://arxiv.org/abs/math/0512385 | |
| dc.identifier | http://arxiv.org/abs/math/0512385 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122202 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 14M25; 52B20 | |
| dc.title | Projective Q-factorial toric varieties covered by lines | |
| dc.type | text |