This thesis studies numerically flat Higgs bundles on complex projective manifolds, motivated by Bruzzo's conjecture about the vanishing of their Chern classes, and their consequent speculative relationship to harmonic bundles. The themes developed are: the spectral cover and the Grassmannian of Higgs quotients as a Quot scheme; Tannakian categories of decorated bundles and extensions of Langer's S-fundamental group scheme; families of harmonic bundles and the Gauss-Manin derivative; jump deformations of algebraic structures from the point of view of derived algebraic geometry.

On numerically flat Higgs bundles / Sorrentino, Francesco. - (2019 Jan 31).

On numerically flat Higgs bundles

Sorrentino, Francesco
2019

Abstract

This thesis studies numerically flat Higgs bundles on complex projective manifolds, motivated by Bruzzo's conjecture about the vanishing of their Chern classes, and their consequent speculative relationship to harmonic bundles. The themes developed are: the spectral cover and the Grassmannian of Higgs quotients as a Quot scheme; Tannakian categories of decorated bundles and extensions of Langer's S-fundamental group scheme; families of harmonic bundles and the Gauss-Manin derivative; jump deformations of algebraic structures from the point of view of derived algebraic geometry.
Bruzzo, Ugo
Bartocci, Claudio; Rubtsov, Vladimir
Sorrentino, Francesco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/86570
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