Stable Higgs bundles over positive principal elliptic fibrations

Let M be a compact complex manifold of dimension at least three and Π : M → X a positive principal elliptic fibration, where X is a compact Kähler orbifold. Fix a preferred Hermitian metric on M. In [14], the third author proved that every stable vector bundle on M is of the form L⊕ Π ⃰ B0, where B0...

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Autores principales:	Biswas Indranil, Mj Mahan, Verbitsky Misha
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2018
Materias:	principal elliptic fibration higgs bundle preferred metric yang-mills equation positivity Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/27d3a56d803442eda9279c7216753c52
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spelling	oai:doaj.org-article:27d3a56d803442eda9279c7216753c522021-12-02T19:08:48ZStable Higgs bundles over positive principal elliptic fibrations2300-744310.1515/coma-2018-0012https://doaj.org/article/27d3a56d803442eda9279c7216753c522018-11-01T00:00:00Zhttps://doi.org/10.1515/coma-2018-0012https://doaj.org/toc/2300-7443Let M be a compact complex manifold of dimension at least three and Π : M → X a positive principal elliptic fibration, where X is a compact Kähler orbifold. Fix a preferred Hermitian metric on M. In [14], the third author proved that every stable vector bundle on M is of the form L⊕ Π ⃰ B0, where B0 is a stable vector bundle on X, and L is a holomorphic line bundle on M. Here we prove that every stable Higgs bundle on M is of the form (L ⊕ Π ⃰B0, Π ⃰ ɸX), where (B0, ɸX) is a stable Higgs bundle on X and L is a holomorphic line bundle on M.Biswas IndranilMj MahanVerbitsky MishaDe Gruyterarticleprincipal elliptic fibrationhiggs bundlepreferred metricyang-mills equationpositivityMathematicsQA1-939ENComplex Manifolds, Vol 5, Iss 1, Pp 195-201 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	principal elliptic fibration higgs bundle preferred metric yang-mills equation positivity Mathematics QA1-939
spellingShingle	principal elliptic fibration higgs bundle preferred metric yang-mills equation positivity Mathematics QA1-939 Biswas Indranil Mj Mahan Verbitsky Misha Stable Higgs bundles over positive principal elliptic fibrations
description	Let M be a compact complex manifold of dimension at least three and Π : M → X a positive principal elliptic fibration, where X is a compact Kähler orbifold. Fix a preferred Hermitian metric on M. In [14], the third author proved that every stable vector bundle on M is of the form L⊕ Π ⃰ B0, where B0 is a stable vector bundle on X, and L is a holomorphic line bundle on M. Here we prove that every stable Higgs bundle on M is of the form (L ⊕ Π ⃰B0, Π ⃰ ɸX), where (B0, ɸX) is a stable Higgs bundle on X and L is a holomorphic line bundle on M.
format	article
author	Biswas Indranil Mj Mahan Verbitsky Misha
author_facet	Biswas Indranil Mj Mahan Verbitsky Misha
author_sort	Biswas Indranil
title	Stable Higgs bundles over positive principal elliptic fibrations
title_short	Stable Higgs bundles over positive principal elliptic fibrations
title_full	Stable Higgs bundles over positive principal elliptic fibrations
title_fullStr	Stable Higgs bundles over positive principal elliptic fibrations
title_full_unstemmed	Stable Higgs bundles over positive principal elliptic fibrations
title_sort	stable higgs bundles over positive principal elliptic fibrations
publisher	De Gruyter
publishDate	2018
url	https://doaj.org/article/27d3a56d803442eda9279c7216753c52
work_keys_str_mv	AT biswasindranil stablehiggsbundlesoverpositiveprincipalellipticfibrations AT mjmahan stablehiggsbundlesoverpositiveprincipalellipticfibrations AT verbitskymisha stablehiggsbundlesoverpositiveprincipalellipticfibrations
_version_	1718377137222713344

Stable Higgs bundles over positive principal elliptic fibrations

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