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2019 Relative algebro-geometric stabilities of toric manifolds
Naoto Yotsutani, Bin Zhou
Tohoku Math. J. (2) 71(4): 495-524 (2019). DOI: 10.2748/tmj/1576724790

Abstract

In this paper we study the relative Chow and $K$-stability of toric manifolds. 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 [34], which fits into the relative GIT stability detected by Székelyhidi. The other way relies on $\mathbb{C}^*$-actions and Chow weights associated to toric degenerations following Donaldson and Ross-Thomas [13, 36]. In the end, we determine the relative $K$-stability of all toric Fano threefolds and present counter-examples which are relatively $K$-stable in the toric sense but which are asymptotically relatively Chow unstable.

Citation

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Naoto Yotsutani. Bin Zhou. "Relative algebro-geometric stabilities of toric manifolds." Tohoku Math. J. (2) 71 (4) 495 - 524, 2019. https://doi.org/10.2748/tmj/1576724790

Information

Published: 2019
First available in Project Euclid: 19 December 2019

zbMATH: 07199976
MathSciNet: MR4043922
Digital Object Identifier: 10.2748/tmj/1576724790

Subjects:
Primary: 53C55
Secondary: 14L24, 14M25

Rights: Copyright © 2019 Tohoku University

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Vol.71 • No. 4 • 2019
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