On the slope conjecture of Barja and Stoppino for fibred surfaces

Abstract

Let $f:S\to B$ be a locally non-trivial relatively minimal fibration of genus $g\ge 2$ with relative irregularity $q_f$. It was conjectured by Barja and Stoppino that the slope ${\lambda }_f\ge \frac{4(g-1)}{g-q_f}$. We prove the conjecture when $q_f$ is small with respect to $g$; we also construct counterexamples when $g$ is odd and $q_f=(g+1)/2$.

any comment is welcome

References in corpus (2)

• On the Severi type inequalities for irregular surfaces
• On the slope of hyperelliptic fibrations with positive relative irregularity

Cited by in corpus (3)

• Surfaces of general type with q=2 are rigidified
• On the Severi type inequalities for irregular surfaces
• Slope inequalities for irregular cyclic covering fibrations