On the slope of fourgonal semistable fibrations
Valentina Beorchia, Francesco Zucconi
TL;DR
This paper establishes bounds on the slope of sweeping curves within the fourgonal locus of the moduli space of genus g algebraic curves, using inequalities related to vector bundles on ruled surfaces.
Contribution
It introduces new bounds on the slope in the fourgonal locus by applying Bogomolov-type inequalities to vector bundles on ruled surfaces.
Findings
Bounded the slope of sweeping curves in the fourgonal locus.
Derived inequalities for rank two vector bundles on ruled surfaces.
Provided new insights into the geometry of the moduli space.
Abstract
We bound the slope of sweeping curves in the fourgonal locus of the moduli space of genus g algebraic curves. Our results follow from some Bogomolov-type inequalities for weakly positive rank two vector bundles on ruled surfaces.
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