Zobrazeno 1 - 10
of 340
pro vyhledávání: '"P, Hitchin"'
Autor:
Hitchin, Nigel
We investigate the geometry of holomorphic vector bundles $E$ over a Riemann surface $C$ together with a section of the endomorphism bundle tensored with $K^{1/2}$ -- a square root of the canonical bundle $K$. These parallel to some extent the variou
Externí odkaz:
http://arxiv.org/abs/2404.12981
Autor:
Hitchin, Nigel
We consider the twistor theory approach to Kronheimer's ALE metrics on resolutions of the quotient of C^2 by a finite subgroup of SU(2). The circle action on the 4-manifold induces a C^* action on a compactification of the twistor space and we identi
Externí odkaz:
http://arxiv.org/abs/2402.04021
Autor:
Hitchin, Nigel
Publikováno v:
SIGMA 19 (2023), 003, 9 pages
The article considers some concrete solutions to the Dirac equation coupled to a vector bundle with connection, arising in the study of Yang-Mills equations and vector bundles on Riemann surfaces.
Comment: Dedicated to Jean-Pierre Bourguignon on
Comment: Dedicated to Jean-Pierre Bourguignon on
Externí odkaz:
http://arxiv.org/abs/2210.17512
Autor:
Hitchin, Nigel
Hausel introduced a commutative algebra -- the multiplicity algebra -- associated to a fixed point of the C^*-action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector bundle an
Externí odkaz:
http://arxiv.org/abs/2203.03424
Autor:
Hitchin, Nigel
We use the notion of the principal three-dimensional subgroup of a simple Lie group to identify certain special subspaces of the Lie algebra and address the question of whether these are calibrated for invariant forms on the group.
Comment: Dedi
Comment: Dedi
Externí odkaz:
http://arxiv.org/abs/2201.06331
Autor:
Hitchin, Nigel J.
Publikováno v:
SIGMA 17 (2021), 090, 9 pages
The paper studies explicitly the Hitchin system restricted to the Higgs fields on a fixed very stable rank 2 bundle in genus 2 and 3. The associated families of quadrics relate to both the geometry of Penrose's twistor spaces and several classical re
Externí odkaz:
http://arxiv.org/abs/2108.02603
Autor:
Hausel, Tamas, Hitchin, Nigel
We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. The main ing
Externí odkaz:
http://arxiv.org/abs/2101.08583
Autor:
Hitchin, Nigel
We first describe the action of the fundamental group of a closed surface of variable negative curvature on the oriented geodesics in its universal covering in terms of a naturally-defined flat connection whose holonomy lies in the group of Hamiltoni
Externí odkaz:
http://arxiv.org/abs/2010.07186
Autor:
Hitchin, Nigel
This paper focuses on the spherical fixed point set of a circle action on an ALE space endowed with Kronheimer's hyperkaehler metric. The induced metric on the sphere is described by using the algebraic geometry of rational curves on algebraic surfac
Externí odkaz:
http://arxiv.org/abs/2008.05915
Autor:
Hitchin, Nigel
We describe the Special K\"ahler structure on the base of the so-called Hitchin system in terms of the geometry of the space of spectral curves. It yields a simple formula for the K\"ahler potential. This extends to the case of a singular spectral cu
Externí odkaz:
http://arxiv.org/abs/1910.05170