A sharp bound on the number of real intersection points of a sparse plane curve with a line

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• 作者：Fré ; dé ; ric Bihan ^{Frederic.Bihan@univ-smb.fr} ; Boulos El Hilany ^{boulos.el-hilany@univ-smb.fr}
• 关键词：14T05
• 刊名：Journal of Symbolic Computation
• 出版年：2017
• 出版时间：July-August 2017
• 年：2017
• 卷：81
• 期：Complete
• 页码：88-96
• 全文大小：316 K
• 卷排序：81

文摘

We prove that the number of real intersection points of a real line with a real plane curve defined by a polynomial with at most t   monomials is either infinite or does not exceed 6t−76t−7. This improves a result by M. Avendaño. Furthermore, we prove that this bound is sharp for t=3t=3 with the help of Grothendieck's dessins d'enfant.