4 problems

Xiao's conjecture. The sharper bound

Let $f\colon S \longrightarrow B$ be a fibration of genus $g$, and let $q_f$ denote its relative irregularity, with $q_f<g-1$. The slope $s(f)$ is the ratio of the relevant relativ…

Barja–González–Naranjo's modified conjecture. For every non-isotrivial fibred surface $f\colon S\to B$ of genus $g\geq 2$,

Let $f\colon S\to B$ be a fibred surface, meaning a fibration from a smooth projective surface $S$ to a smooth projective curve $B$, with general fibre of genus $g\geq 2$. Let…