Hilbert series and obstructions to asymptotic semistability
Hilbert series and obstructions to asymptotic semistability
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希尔伯特级数和渐近半稳定性的障碍
DOI：
10.1016/j.aim.2010.06.018
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
H.Ono and Y.Sano
中科院分区：
文献类型：
--
作者：
A.Futaki;H.Ono and Y.Sano
给定一个极化流形，用积分不变量描述的渐近Chow半稳定性存在障碍，而积分不变量可以看作是全纯向量场李代数的特征。在本文中，我们表明，在环面Fano流形，这些李代数特征的线性跨度与希尔伯特级数的洛朗级数的导数一致。
Given a polarized manifold there are obstructions for asymptotic Chow semistability described as integral invariants which can be regarded as characters of the Lie algebra of holomorphic vector fields. In this paper we show that, on toric Fano manifolds, the linear span of those Lie algebra characters coincides with the derivatives of the Laurent series of the Hilbert series.