# Geometria em Lisboa Seminar

### On a conjecture about curve semistable Higgs bundles

We say that a Higgs bundle $E$ over a projective variety $X$ is curve semistable if for every morphism $f : C \to X$, where $C$ is a smooth irreducible projective curve, the pullback $f^\ast E$ is semistable. We study this class of Higgs bundles, reviewing the status of a conjecture about their Chern classes.

Current organizer: Rosa Sena Dias