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Relative Algebro-Geometric stabilities o...
Yotsutani, Naoto...

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Relative Algebro-Geometric stabilities of Toric Manifolds by Yotsutani, Naoto ( Author )
Lemonjar Open Access
N.A
26-02-2016
In this paper we study the relative Chow and K-stability of toric manifolds in the toric sense. First, we give a criterion for relative K-stability and instability of toric Fano manifolds in the toric sense. The reduction of relative Chow stability on toric manifolds will be investigated using the Hibert-Mumford criterion in two ways. One is to consider the maximal torus action and its weight polytope. We obtain a reduction by the strategy of Ono [Ono13], which fits into the relative GIT stability detected by Székelyhidi. The other way relies on C∗-actions and Chow weights associated to toric degenerations following Donaldson and Ross-Thomas [D02, RT07]. As applications of our main theorem, we partially determine the relative K-stability of toric Fano threefolds and present counter-examples which are relatively K-stable in the toric sense but which are asymptotically relatively Chow unstable. In the end, we explain the erroneous parts of the published version of this article (corresponding to Sections 1-5), which provides some inconclusive results for relative K-stability in Table 6.
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Article
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English
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MYR 0.01
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https://arxiv.org/abs/1602.08201
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