Rational cuspidal curves with four cusps on Hirzebruch surfaces
| Autor: | Torgunn Karoline Moe |
|---|---|
| Jazyk: | English<br />French<br />Italian |
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Le Matematiche, Vol 69, Iss 2, Pp 295-318 (2014) |
| Druh dokumentu: | article |
| ISSN: | 0373-3505 2037-5298 |
| Popis: | The purpose of this article is to shed light on the question of how many and what kind of cusps a rational cuspidal curve on a Hirzebruch surface can have. Our main result is a list of rational cuspidal curves with four cusps, their type, cuspidal congurations and the surfaces they lie on. We use birational transformations to construct these curves. Moreover, we find a general expression for and compute the Euler characteristic of the logarithmic tangent sheaf in these cases. Additionally, we show that there exists a real rational cuspidal curve with four real cusps. Last, we show that for rational cuspidal curves with two or more cusps on a Hirzebruch surface, there is a lower bound on one of the multiplicities. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|