Higgs bundles and fundamental group schemes
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Indranil Biswas
und
Sudarshan Gurjar
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.
Acknowledgements
We thank Beatriz Graña Otero and Valeriano Lanza for useful discussions.
Communicated by: G. Gentili
Funding: I. B. is supported by a J. C. Bose Fellowship. U. B.’s research is partly supported by INdAM-GNSAGA. S. G. would like to thank the International Centre for Theoretical Physics, Trieste for a year-long postdoctoral position during which time the project was initiated. The project continued when the author visited the Centre for Quantum Geometry of Moduli Spaces, Aarhus, supported by a Center of Excellence grant from the Danish National Research Foundation (DNRF95) and by a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Union Framework Programme (FP7/2007-2013) under grant agreement n 612534, project MODULI - Indo European Collaboration on Moduli Spaces. He would like to thank the Center for their hospitality.
U. B. is a member of VBAC.
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Artikel in diesem Heft
- Frontmatter
- A remark on the mixed scalar curvature of a manifold with two orthogonal totally umbilical distributions
- On mixed Lp John ellipsoids
- Valuations on convex functions and convex sets and Monge–Ampère operators
- Weierstrass points on Kummer extensions
- The Bonnet problem for harmonic maps to the three-sphere
- Maximal arcs in projective planes of order 16 and related designs
- On the decomposition of the small diagonal of a K3 surface
- Doubly transitive dimensional dual hyperovals: universal covers and non-bilinear examples
- Higgs bundles and fundamental group schemes
- A relation between the curvature ellipse and the curvature parabola
- Non-orientable three-submanifolds of G2-manifolds
- The growth of the first non-Euclidean filling volume function of the quaternionic Heisenberg group
- A class of analytic pairs of conjugate functions in dimension three
Artikel in diesem Heft
- Frontmatter
- A remark on the mixed scalar curvature of a manifold with two orthogonal totally umbilical distributions
- On mixed Lp John ellipsoids
- Valuations on convex functions and convex sets and Monge–Ampère operators
- Weierstrass points on Kummer extensions
- The Bonnet problem for harmonic maps to the three-sphere
- Maximal arcs in projective planes of order 16 and related designs
- On the decomposition of the small diagonal of a K3 surface
- Doubly transitive dimensional dual hyperovals: universal covers and non-bilinear examples
- Higgs bundles and fundamental group schemes
- A relation between the curvature ellipse and the curvature parabola
- Non-orientable three-submanifolds of G2-manifolds
- The growth of the first non-Euclidean filling volume function of the quaternionic Heisenberg group
- A class of analytic pairs of conjugate functions in dimension three
