Bounds of incidences between points and algebraic curves

2013/08/05 by Hong Wang, Ben Yang, Wang, Hong +3 · 3 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.1308.0861

Abstract

We prove new bounds on the number of incidences between points and higher degree algebraic curves. The key ingredient is an improved initial bound, which is valid for all fields. Then we apply the polynomial method to obtain global bounds on ℝ and ℂ.

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• Exposition of Elekes Szabo paper
• Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory
• Distinct distances between a collinear set and an arbitrary set of\n points

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