正主椭圆纤维上的稳定Higgs丛

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2018-06-11 DOI:10.1515/coma-2018-0012

I. Biswas, Mahan Mj, M. Verbitsky

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引用次数: 1

摘要

摘要设M是一个维数至少为3的紧致复流形→ X是正主椭圆fibration，其中X是紧Kähler轨道折叠。在[14]中，第三作者证明了M上的每一个稳定向量丛的形式都是LŞ⃰ B0，其中B0是X上的稳定向量丛，L是M上的全纯线丛⃰B0，π⃰ ΦX），其中（B0，ΦX）是X上的稳定Higgs丛，L是M上的全纯线丛。

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Stable Higgs bundles over positive principal elliptic fibrations

Abstract 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.

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.