2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157956Let $f:S \fr B$ be a surface fibration with fibres of genus 5. We find a linear relation between the fundamental invariants of the surface. Namely $K_f^2=χ_f+N$ where $N$ is the number of trigonal fibres. Our proof is based on the analysis of the relative canonical algebra $\cal{R}(f)$.13 pagesAlgebraic Geometrytext