3 problems

Let $\delta\geq 2$. For a polynomial $g\in\mathbb{Z}[T_1,\ldots,T_\nu]$, let $\mathfrak{h}(g)$ denote its homogeneous part of maximal degree, and let $\mathcal{J}_\delta$ be the se…

Let $F$ be a field of characteristic zero and let $S_F$ be a normal affine surface over $F$. Suppose that $f,g\rbrace\in\operatorname{Aut}(S_F)$ are loxodromic automorphisms. Stron…

Let $C\subset\mathbb{P}^2_{\mathbb{C}}$ be an irreducible curve. A curve is of type I if there exists a point $a\in C$ such that $C\backslash a$ is isomorphic to the affine line; a…