The slope of fibred surfaces: unitary rank and Clifford index

TL;DR

This paper establishes new inequalities relating the slope of fibred surfaces to invariants like irregularity, unitary rank, and Clifford index, using Xiao's method and novel Clifford-type inequalities.

Contribution

It introduces new slope inequalities for fibred surfaces that incorporate the effects of relative irregularity, unitary rank, and Clifford index, with a new Clifford-type inequality for non-hyperelliptic curves.

Findings

Derived slope inequalities involving irregularity, unitary rank, and Clifford index.

Developed a new Clifford-type inequality for subcanonical systems on non-hyperelliptic curves.

Applied Xiao's method to establish these new bounds.

Abstract

We prove new slope inequalities for relatively minimal fibred surfaces, showing an influence of the relative irregularity, of the unitary rank and of the Clifford index on the slope. The argument uses Xiao's method and a new Clifford-type inequality for subcanonical systems on non-hyperelliptic curves.