2015/02/18 by József Solymosi, Solymosi, József, Frank de Zeeuw +1
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1502.05304
openalex publication_date 2015/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove bounds on the number of incidences between a set of algebraic curves in ℂ2 and a Cartesian product A× B with finite sets A,B⊂ ℂ. Similar bounds are known under various conditions, but we show that the Cartesian product assumption leads to a simpler proof. This assumption holds in a number of interesting applications, and with our bound these applications can be extended from ℝ to ℂ. The proof is a new application of the polynomial partitioning technique introduced by Guth and Katz.