Real Zeuthen numbers for two lines
| dc.creator | Bertrand, Benoit | |
| dc.date | 2007-10-04 | |
| dc.date.accessioned | 2026-07-07T08:34:18Z | |
| dc.date.available | 2026-07-07T08:34:18Z | |
| dc.description | Given three natural numbers $k,l,d$ such that $k+l=d(d+3)/2$, the Zeuthen number $N_{d}(l)$ is the number of nonsingular complex algebraic curves of degree $d$ passing through $k$ points and tangent to $l$ lines in $\PP^2$. It does not depend on the generic configuration $C$ of points and lines chosen. If the points and lines are real, the corresponding number $N_{d}^\RR(l,C)$ of real curves usually depends on the configuration chosen. We use Mikhalkin's tropical correspondence theorem to prove that for two lines the real Zeuthen problem is maximal: there exists a configuration $C$ such that $N_{d}^\RR(2,C)=N_{d}(2)$. The correspondence theorem reduces the computation to counting certain lattice paths with multiplicities. | |
| dc.description | 6 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/0710.1095 | |
| dc.identifier | http://arxiv.org/abs/0710.1095 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139390 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14P99; 14N10 | |
| dc.title | Real Zeuthen numbers for two lines | |
| dc.type | text |