Armando Capasso
After recalling the basic notions concerning Higgs-Grassmann schemes, we review how these can be used to define generalisations of the notion of positivity conditions, such as numerical flatness, which “feel” the Higgs field. Then we prove several properties of Higgs bundles over smooth projective varieties defined over an algebraically closed field of characteristic 0, satisfying these conditions. Finally, we discuss how one can relate them to semistability of the so-called “curve semistable” Higgs bundles.