CONSTRUCTING CO-HIGGS BUNDLES ON ℂℙ2
CONSTRUCTING CO-HIGGS BUNDLES ON ℂℙ2
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在 ℂℙ2 上构建 CO-HIGS 束
DOI：
10.1093/qmath/hau017
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发表时间：
2013
影响因子：
0.7
通讯作者：
S. Rayan
中科院分区：
文献类型：
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作者：
S. Rayan
在复流形上，co-Higgs丛是一个全纯向量丛，其自同态被切丛扭曲。当广义复流形是普通复流形时，Hitchin广义几何中的广义全纯丛与co-Higgs丛的概念是一致的。施瓦岑伯格在射影平面上的秩为2的向量丛，由双覆盖CP ^1\times CP ^1\to CP ^2上的线丛构造而成，自然是一个co-Higgs丛，其扭曲自同态，或“Higgs场”，也从双覆盖中产生。允许分支圆锥曲线变化，我们发现Schwarzenberger丛产生一个8维模空间的co-Higgs丛。在研究了复流形上co-Higgs丛的形变理论之后，我们得出结论：从具有非零Higgs场的Schwarzenberger丛产生的co-Higgs丛是刚性的，在这个意义上，附近的形变又是Schwarzenberger的.
On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with an endomorphism twisted by the tangent bundle. The notion of generalized holomorphic bundle in Hitchin's generalized geometry coincides with that of co-Higgs bundle when the generalized complex manifold is ordinary complex. Schwarzenberger's rank-2 vector bundle on the projective plane, constructed from a line bundle on the double cover CP^1 \times CP^1 \to CP^2, is naturally a co-Higgs bundle, with the twisted endomorphism, or "Higgs field", also descending from the double cover. Allowing the branch conic to vary, we find that Schwarzenberger bundles give rise to an 8-dimensional moduli space of co-Higgs bundles. After studying the deformation theory for co-Higgs bundles on complex manifolds, we conclude that a co-Higgs bundle arising from a Schwarzenberger bundle with nonzero Higgs field is rigid, in the sense that a nearby deformation is again Schwarzenberger.
(7)有理椭圆面的Q分裂模型
DOI：
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发表时间：
2006
期刊：
影响因子：
--
作者：
塩田 徹治;筧 三郎;覧 三郎;筧 三郎;筧 三郎;塩田 徹治;塩田 徹治;塩田 徹治;塩田 徹治
通讯作者：
塩田 徹治