Relying on a notion of ``numerical effectiveness'' for Higgs bundles, we show that the category of ``numerically flat'' Higgs vector bundles on a smooth projective variety $X$ is a Tannakian category. We introduce the associated group scheme, that we call the ``Higgs fundamental group scheme of $X$,'' and show that its properties are related to a conjecture about the vanishing of the Chern classes of numerically flat Higgs vector bundles.

Higgs bundles and fundamental group schemes / Biswas, I.; Bruzzo, U.; Gurjar, S.. - In: ADVANCES IN GEOMETRY. - ISSN 1615-715X. - 19:3(2019). [10.1515/advgeom-2018-0035]

Higgs bundles and fundamental group schemes

Bruzzo, U.
Membro del Collaboration group
;
2019

Abstract

Relying on a notion of ``numerical effectiveness'' for Higgs bundles, we show that the category of ``numerically flat'' Higgs vector bundles on a smooth projective variety $X$ is a Tannakian category. We introduce the associated group scheme, that we call the ``Higgs fundamental group scheme of $X$,'' and show that its properties are related to a conjecture about the vanishing of the Chern classes of numerically flat Higgs vector bundles.
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Biswas, I.; Bruzzo, U.; Gurjar, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/85854
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