# The gradient flow of Higgs pairs

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 5, page 1373-1422
- ISSN: 1435-9855

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topLi, Jiayu, and Zhang, Xi. "The gradient flow of Higgs pairs." Journal of the European Mathematical Society 013.5 (2011): 1373-1422. <http://eudml.org/doc/277241>.

@article{Li2011,

abstract = {We consider the gradient flow of the Yang–Mills–Higgs functional of Higgs pairs on a Hermitian vector bundle $(E,H_0)$ over a Kähler surface $(M,\omega )$, and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition
$(A_0,\phi _0)$ converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point $(A_\infty ,\phi _\infty )$ of this functional. We also prove that the limiting Higgs pair $(A_\infty ,\phi _\infty )$ can be extended smoothly to a vector bundle $E_\infty $ over $(M,\omega )$, and the isomorphism class of the limiting Higgs bundle $(E_\infty ,A_\infty \phi _\infty )$ is given by the double dual of the graded Higgs sheaves
associated to the Harder–Narasimhan–Seshadri filtration of the initial Higgs bundle $(E,A_0,\phi _0)$.},

author = {Li, Jiayu, Zhang, Xi},

journal = {Journal of the European Mathematical Society},

keywords = {Higgs bundles; Kähler surface; Harder–Narasimhan–Seshadri filtration; Higgs bundles, Kähler surface, Harder-Narasimhan-Seshadri filtration},

language = {eng},

number = {5},

pages = {1373-1422},

publisher = {European Mathematical Society Publishing House},

title = {The gradient flow of Higgs pairs},

url = {http://eudml.org/doc/277241},

volume = {013},

year = {2011},

}

TY - JOUR

AU - Li, Jiayu

AU - Zhang, Xi

TI - The gradient flow of Higgs pairs

JO - Journal of the European Mathematical Society

PY - 2011

PB - European Mathematical Society Publishing House

VL - 013

IS - 5

SP - 1373

EP - 1422

AB - We consider the gradient flow of the Yang–Mills–Higgs functional of Higgs pairs on a Hermitian vector bundle $(E,H_0)$ over a Kähler surface $(M,\omega )$, and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition
$(A_0,\phi _0)$ converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point $(A_\infty ,\phi _\infty )$ of this functional. We also prove that the limiting Higgs pair $(A_\infty ,\phi _\infty )$ can be extended smoothly to a vector bundle $E_\infty $ over $(M,\omega )$, and the isomorphism class of the limiting Higgs bundle $(E_\infty ,A_\infty \phi _\infty )$ is given by the double dual of the graded Higgs sheaves
associated to the Harder–Narasimhan–Seshadri filtration of the initial Higgs bundle $(E,A_0,\phi _0)$.

LA - eng

KW - Higgs bundles; Kähler surface; Harder–Narasimhan–Seshadri filtration; Higgs bundles, Kähler surface, Harder-Narasimhan-Seshadri filtration

UR - http://eudml.org/doc/277241

ER -

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