Constructive Polynomial Partitioning for Algebraic Curves in ${\mathbb{R}}^3$ with Applications

Boris Aronov, Esther Ezra, Joshua Zahl

In 2015, Guth proved that for any set of $k$-dimensional bounded complexity varieties in ${\mathbb{R}}^d$ and for any positive integer $D$, there exists a polynomial of degree at mos…