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biodiversitylibrary.org

the biodiversity heritage library works collaboratively to make biodiversity literature openly available to the world as part of a global biodiversity community.

projecteuclid.org

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.

journals.plos.org

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onlinelibrary.wiley.com

one of the largest and most authoritative collections of online journals, books, and research resources, covering life, health, social, and physical sciences.

link.springer.com

providing access to millions of research articles and chapters from science, technology and medicine, and humanities and social sciences

sciencedirect.com

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academic.oup.com

Oxford Academic

pnas.org

proceedings of the national academy of sciences (pnas), a peer reviewed journal of the national academy of sciences (nas) - an authoritative source of high-impact, original research that broadly spans the biological, physical, and social sciences.

royalsocietypublishing.org

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mdpi.com

MDPI is a publisher of peer-reviewed, open access journals since its establishment in 1996.