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Article

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Accepted version

Publication date

2015-08

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cc-by-nc-nd (c) Elsevier B.V., 2015
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/102010

On the intersection of ACM curves in $\mathbb{P}$

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http://dx.doi.org/10.1016/j.jpaa.2014.10.009

Abstract

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.

Subject

Geometria algebraica, Corbes

Subject (English)

Algebraic geometry, Curves

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

HARTSHORNE, Robin and MIRÓ-ROIG, Rosa M. (Rosa Maria). On the intersection of ACM curves in $\mathbb{P}$. Journal of Pure and Applied Algebra. 2015. Vol. 219, num. 8, pags. 3195-3213. ISSN 0022-4049. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/102010

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