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arXiv · 1811.07865

The polynomial method over varieties

Miguel N. Walsh
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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.

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Miguel N. Walsh. 2020-06-12. The polynomial method over varieties. https://arxiv.org/abs/1811.07865

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