The number of plane conics 5-fold tangent to a given curve
| dc.creator | Gathmann, Andreas | |
| dc.date | 2002-01-31 | |
| dc.date.accessioned | 2026-07-07T04:46:15Z | |
| dc.date.available | 2026-07-07T04:46:15Z | |
| dc.description | Given a general plane curve Y of degree d, we compute the number n_d of irreducible plane conics that are 5-fold tangent to Y. This problem has been studied before by Vainsencher using classical methods, but it could not be solved there because the calculations received too many non-enumerative correction terms that could not be analyzed. In our current approach, we express the number n_d in terms of relative Gromov-Witten invariants that can then be directly computed. As an application, we consider the K3 surface given as the double cover of P^2 branched along a sextic curve. We compute the number of rational curves in this K3 surface in the homology class that is the pull-back of conics in P^2, and compare this number to the corresponding Yau-Zaslow K3 invariant. This gives an example of such a K3 invariant for a non-primitive homology class. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0202002 | |
| dc.identifier | http://arxiv.org/abs/math/0202002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63254 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The number of plane conics 5-fold tangent to a given curve | |
| dc.type | text |