On the intersection of ACM curves in P3

• Robin Hartshorne ^[2] ; Rosa M. Miró-Roig ^[1]
  1. [1] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
  2. [2] University of California, USA
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 8 (August 2015), 2015, págs. 3195-3213
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.10.009
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• Resumen

  • Bezout's theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in P3 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 P3. The bound that we give is in many cases optimal as a function of only the degrees and the initial degrees of the curves.