On the intersection of ACM curves in $\mathbb{P}$
Bezout's theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in $\mathbb{P}$ never intersect properly, Bezout's theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the max...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/102010 |
| Acceso en línea: | https://hdl.handle.net/2445/102010 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometria algebraica Corbes Algebraic geometry Curves |
| Sumario: | Bezout's theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in $\mathbb{P}$ never intersect properly, Bezout's theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the maximum number of intersection points of two integral ACM curves in $\mathbb{P}$. The bound that we give is in many cases optimal as a function of only the degrees and the initial degrees of the curves. |
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