Bounds of incidences between points and algebraic curves

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 $\mathbb{C}$.

11 pages

References in corpus (1)

• On the Erdos distinct distance problem in the plane

Cited by in corpus (5)

• Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory
• Exposition of Elekes Szabo paper
• Ramsey-type theorems for lines in 3-space
• Multilevel polynomial partitions and simplified range searching
• Distinct distances between a collinear set and an arbitrary set of points