Bounds of incidences between points and algebraic curves

Hong Wang; Ben Yang; Ruixiang Zhang

Bounds of incidences between points and algebraic curves

Combinatorics 2015-03-31 v3

Authors: Hong Wang , Ben Yang , Ruixiang Zhang

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 $\mathbb{R}$ and $\mathbb{C}$ .

Keywords

incidence bounds algebraic curves polynomial method combinatorial geometry fields

Cite

@article{arxiv.1308.0861,
  title  = {Bounds of incidences between points and algebraic curves},
  author = {Hong Wang and Ben Yang and Ruixiang Zhang},
  journal= {arXiv preprint arXiv:1308.0861},
  year   = {2015}
}

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11 pages

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