The geometry and topology of toric hyperkahler manifolds
The geometry and topology of toric hyperkahler manifolds
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环面超卡勒流形的几何和拓扑
DOI：
10.4310/cag.2000.v8.n4.a2
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发表时间：
2000
影响因子：
0.7
通讯作者：
A. Dancer
中科院分区：
文献类型：
--
作者：
R. Bielawski;A. Dancer
我们研究了超Kahler流形，它可以通过环面作为平坦四元数空间的超Kahler流形，特别是它们与环面簇和Delzant多面体的关系。当光滑时，这些超卡勒反射是完整的。我们还证明了对于光滑的投射环面簇X，X的余切丛带有超Kahler度量，它是完备的，仅当X是投射空间的乘积.我们的超卡勒流形具有紧复曲面簇与沿着复曲面子簇相交的并的同伦类型。给出了超Kahler度规及其Kahler势的显式表达式。
We study hyperkahler manifolds that can be obtained as hyperkahler quotients of flat quaternionic space by tori, and in particular, their relation to toric varieties and Delzant polytopes. When smooth, these hyperkahler quotients are complete. We also showthat for smooth projective toric varieties X the cotangent bundle of X carries a hyperkahler metric, which is complete only if X is a product of projective spaces. Our hyperkahler manifolds have the homotopy type of a union of compact toric varieties intersecting along toric subvarieties. We give explicit formulas for the hyperkahler metric and its Kahler potential.