English

The polynomial method over varieties

Algebraic Geometry 2020-06-15 v2 Combinatorics

Abstract

We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic varieties. As a first application, we provide a general incidence estimate that is tight in its dependence on the size, degree and dimension of the varieties involved.

Keywords

Cite

@article{arxiv.1811.07865,
  title  = {The polynomial method over varieties},
  author = {Miguel N. Walsh},
  journal= {arXiv preprint arXiv:1811.07865},
  year   = {2020}
}

Comments

36 pages

R2 v1 2026-06-23T05:20:59.406Z