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...

Descripción completa

Detalles Bibliográficos
Autores: Hartshorne, Robin, Miró-Roig, Rosa M. (Rosa Maria)
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
Descripción
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.