Counting integral points in thin sets of type II: singularities, sieves, and stratification

Dante Bonolis, Lillian B. Pierce, Katharine Woo

Consider an absolutely irreducible polynomial $F(Y,X_1,\dots ,X_n)\in \mathbb{Z}[Y,X_1,\dots ,X_n]$ that is monic in $Y$ and is a polynomial in $Y^m$ for an integer $m\ge 1$. Le…