Welschinger invariant and enumeration of real plane rational curves
| dc.creator | Itenberg, I. | |
| dc.creator | Kharlamov, V. | |
| dc.creator | Shustin, E. | |
| dc.date | 2003-03-30 | |
| dc.date | 2003-06-16 | |
| dc.date.accessioned | 2026-07-07T04:56:30Z | |
| dc.date.available | 2026-07-07T04:56:30Z | |
| dc.description | Welschinger's invariant bounds from below the number of real rational curves through a given generic collection of real points in the real projective plane. We estimate this invariant using Mikhalkin's approach which deals with a corresponding count of tropical curves. In particular, our estimate implies that, for any positive integer $d$, there exists a real rational curve of degree $d$ through any collection of $3d-1$ real points in the projective plane, and, moreover, asymptotically in the logarithmic scale at least one third of the complex plane rational curves through a generic point collection are real. We also obtain similar results for curves on other toric Del Pezzo surfaces. | |
| dc.description | 17 pages, LATEX2e; revised version: some statements modified (the case of rational geometrically ruled surfaces is replaced by that of the toric Del Pezzo surfaces), proofs extended, 2 figures added | |
| dc.identifier | https://arxiv.org/abs/math/0303378 | |
| dc.identifier | http://arxiv.org/abs/math/0303378 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66944 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14N10; 14P05 | |
| dc.title | Welschinger invariant and enumeration of real plane rational curves | |
| dc.type | text |