Zobrazeno 1 - 10
of 64
pro vyhledávání: '"Gothen, P. B."'
Autor:
Silva, Pedro M., Gothen, Peter B.
Publikováno v:
International Mathematics Research Notices (2024), no. 16, 11812-11831
The non-abelian Hodge correspondence maps a polystable $\mathrm{SL}(2,\mathbb{R})$-Higgs bundle on a compact Riemann surface $X$ of genus $g\geq2$ to a connection which, in some cases, is the holonomy of a branched hyperbolic structure. On the other
Externí odkaz:
http://arxiv.org/abs/2401.07759
Autor:
Gothen, Peter B.
Publikováno v:
CIM Bulletin 45 (2023), 25-34
There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic case we de
Externí odkaz:
http://arxiv.org/abs/2311.12506
Publikováno v:
International Journal of Mathematics 35 (2024), 2441006
Narasimhan--Ramanan branes were introduced by the authors in a previous article. They consist of a family of $BBB$-branes inside the moduli space of Higgs bundles, and a family of complex Lagrangian subvarieties. It was conjectured that these complex
Externí odkaz:
http://arxiv.org/abs/2302.02736
Publikováno v:
Geometriae Dedicata 217 (2023), Paper No. 27, 41 pp
Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and study a c
Externí odkaz:
http://arxiv.org/abs/2208.09022
Publikováno v:
Revista Matem\'atica Complutense 35 (2022), 311-321
We consider the problem of finding the limit at infinity (corresponding to the downward Morse flow) of a Higgs bundle in the nilpotent cone under the natural $\mathbb{C}^*$-action on the moduli space. For general rank we provide an answer for Higgs b
Externí odkaz:
http://arxiv.org/abs/2006.08837
Akademický článek
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Publikováno v:
Bulletin des Sciences Math\'ematiques, 150 (2019), 84-101
Let $G$ be a real reductive Lie group, and $H^{\mathbb{C}}$ the complexification of its maximal compact subgroup $H\subset G$. We consider classes of semistable $G$-Higgs bundles over a Riemann surface $X$ of genus $g\geq2$ whose underlying $H^{\math
Externí odkaz:
http://arxiv.org/abs/1805.10081
Autor:
Gothen, P. B., Nozad, A.
Publikováno v:
Geometriae Dedicata, 199 (2019), 137-146
Holomorphic chains on a Riemann surface arise naturally as fixed points of the natural C*-action on the moduli space of Higgs bundles. In this paper we associate a new quiver bundle to the Hom-complex of two chains, and prove that stability of the ch
Externí odkaz:
http://arxiv.org/abs/1709.09581
Autor:
Gothen, Peter B., Oliveira, André G.
Publikováno v:
Journal of Geometry and Physics, 137 (2019), 7-34
We prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli space of strongly parabolic Higgs bundles of rank two or three, with full flags. Although the main theorem is proved only for rank at most three, most of the result
Externí odkaz:
http://arxiv.org/abs/1707.08536
Akademický článek
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