Old and new examples of k-nets in P^2
| dc.creator | Stipins, Janis | |
| dc.date | 2007-01-01 | |
| dc.date.accessioned | 2026-07-07T07:37:58Z | |
| dc.date.available | 2026-07-07T07:37:58Z | |
| dc.description | In this paper, we present a number of examples of k-nets, which are special configurations of lines and points in the projective plane. Such a configuration can be regarded as the union of k completely reducible elements of a pencil of complex plane curves; equivalently it can be regarded as a set of k polygons in the complex projective plane that satisfy a condition of mutual perspectivity and nondegenerate intersection. For each example, we describe its construction, combinatorial properties, and parameter space. Most of the examples are historical, although perhaps not very well-known; our only essentially new example is a 3-net of pentagons which does not realize a group. The existence of this example settles a question posed by S. Yuzvinsky. | |
| dc.description | 14 pages. A paper based on a talk given during an MSRI conference on hyperplane arrangements, in honor of Sergey Yuzvinsky | |
| dc.identifier | https://arxiv.org/abs/math/0701046 | |
| dc.identifier | http://arxiv.org/abs/math/0701046 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120962 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 14N20, 52C30; 14H50 | |
| dc.title | Old and new examples of k-nets in P^2 | |
| dc.type | text |