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.
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