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An overview on curve semistable and numerically flat Higgs bundles
Armando Capasso
After recalling the basic notions concerning Higgs-Grassmannian schemes, I review how these later can be used to define generalisations of the notion of positivity conditions, such…
Curve semistable Higgs bundles and smooth projective varieties whose canonical bundle is ample
Armando Capasso
Considering the so-called Simpson system on smooth projective varieties, defined over an algebraically closed field of characteristic 0, whose canonical bundle is ample, I give ano…
Lefschetz principle-type theorems for curve semistable Higgs sheaves and applications to elliptic surfaces
Armando Capasso
I prove ``Lefschetz principle''-type theorems for slope semistable and curve semistable Higgs sheaves on smooth projective varieties, defined over an algebraically closed field of…
Positivity for Higgs vector bundles: criteria and applications
Ugo Bruzzo, Armando Capasso, Beatriz Graña Otero
Working in the category of smooth projective varieties over an algebraically closed field of characteristic 0, we review notions of ampleness and numerical nefness for Higgs bundle…
Vanishing Chern classes for numerically flat Higgs bundles
Armando Capasso
I consider Higgs bundles satisfying a notion of ampleness that was introduce Bruzzo, Graña Otero and Hernández Ruipérez, and prove that the Chern classes of rank H-ample Higgs…
Higgs reductions and numerically flat principal Higgs bundles
Armando Capasso
I consider principal Higgs bundles satisfying a notion of numerical flatness (H-nflatness) that was introduced by Bruzzo and Graña Otero. I prove that a principal Higgs bundle $\ma…
Filtrations of numerically flat Higgs bundles and curve semistable Higgs bundles on Calabi-Yau manifolds
Ugo Bruzzo, Armando Capasso
We consider Higgs bundles satisfying a notion of numerical flatness (H-nflatness) that was previously introduced, and show that they have Jordan-Hölder filtrations whose quotients…